They come with bolts because QR's typcially don't clamp with enough force to keep the wheel from slipping forward.
It looks like you have rear facing dropouts, so you should easily be able to use QR's if you get yourself a Surly Tuggnut .
That little circle on the side of it is a QR adapter.
You just pop it in and then slide your skewer all the way through.
It's not a bad idea to have a chain tensioner anyway.
One on the drive side will help you get the chain tensioned correctly when mounting the wheel.
I personally like to use chain tensioners on both sides so that the wheel doesn't get knocked crooked if I hit a bump.
I've had it happen.
It sucks.
I've used a bunch of chain tensioners and can say from experience that the Tuggnut is by far the easiest to use on the market, partially because it's the only one I've ever found that requires no tools.
It's also the only one I've ever found that has a QR adapter.
The built-in bottle opener is handy too.
After that little rant, I feel I should mention that I am in no way affiliated with Surly.
The tuggnut is just a really good product.
bicycles.stackexchange.com/users/4239/jimchristie
I've always used a quick release for the front of my fixed gear bike, I've only ever used the bolts on the back.
His highness Sir Sheldon Brown says you should be okay to use a quick release with an enclosed cam ( not an exposed cam ) with an acorn nut that has steel teeth ( not aluminum teeth ).
http://sheldonbrown.com/skewers.html disclaimer: there's no guarantee
this is safe with your particular bike, modify with care and be safe.
bicycles.stackexchange.com/users/5237/Scott Hillson
Just to add to the other answers, it is my experience that you can't get as secure a fit with a QR skewer as with a nutted axle.
If your bike has track forks (like below), rather than forward facing horizontal dropouts, you can probably get away with this, especially by adding a chain tug to keep the wheel from sliding forward in the rear fork end.
If however your bike is a fixie conversion with an old-school horizontal dropout (like below)
I'd highly advise against using a QR.
The forces exerted when pedalling tend to pull the rear wheel forward relative to the rest of the bike.
The axle nut is the only thing resisting this force.
If this connection isn't tight enough your rear wheel could fall out of the dropouts when in motion.
With a fixed gear drivetrain this is very dangerous for obvious reasons.
You can't use a chain tug to prevent this as they old work for backward-facing track forks.
Images from sheldon brown
bicycles.stackexchange.com/users/5740/harryg
With the horizontal dropout the axle can shift.
You pretty much need the nuts to get a tight enough grip.
But I suspect people have used quick release on a single speed.
So Sheldon states an enclosed cam is good enough - not good enough for me.
I am not buying the historical reasons as I see new bikes with nutted horizontal dropout and still QR on the front.
If they were doing it for historical reason they would nut front and rear.
At some point you need to trust that he manufacturer did it that way for a reason.
I have never seen a manufacturer with QR on a horizontal drop out.
The other factor is alignment.
I typically tighten the non drive side first and tweak the drive side for chain tension.
The other factor is the axle size.
On my single speed the axle/skewer is much larger.
I have never seen a nut on the smaller size and never seen QR for the larger size.
bicycles.stackexchange.com/users/7785/paparazzo
Please note that since those fenders are mounted on the outer side of the frame, your skewers are tightened against the fender brackets instead of tightened directly against the frame.
Therefore the skewer's nut splines and material are not the only thing to look at.
You could of course get a pair of those anti-theft-skewers that you tighten with a wrench to get enough torque...
I would simply just enlarge the hole in the fender bracket to 10mm.
Preferably with a round file, since drilling through an oval hole is cumbersome by hand.
That'd be easiest and most reliable.
No need to swap axles and you could securely tighten your nuts as before.
Discalimer: Modifying the brackets would of course make your fenders un-returnable to the store if they don't fit for some other reason.
bicycles.stackexchange.com/users/13177/Okw
You could avoid interfering with your wheel fastening solution by mounting the guards using P-clips on the seat stays.
bicycles.stackexchange.com/users/7984/Emyr
Don't change the axle assembly just to fit mudguards!!
Adapt the mudguards instead.
As pointed out lockuts secure the wheel with much greater force than skewers.
I have these mudguards and whilst they are suited for use with skewers you need to use an adapter with a bigger hole to fit them.
Alternatively direct mount the mudguards to the frame.
bicycles.stackexchange.com/users/37525/OS2
I recently purchased a fixed gear bike,  Kilo TT . I had some fenders lying around,  SKS raceblade . I tried to install them on my bikebut noticed that the fenders attached to the skewers. My fixed gear bike has bolts in the front and back and the fenders only fit quick release skewers.   What are some options? Can I put QR skewers on a fixed gear bike? Is there a reason they come with bolts?
Quick Release on Fixed Gear Bike
bicycles.stackexchange.com
<fixed-gear><fenders><quick-release><skewer>
bicycles.stackexchange.com/questions/23972
bicycles.stackexchange.com/users/11513/bdeonovic
The fenders come with bolts because QR's typcially don't clamp with enough force to keep the wheel from slipping forward.  With rear facing dropouts, you should easily be able to use QR's if you get yourself a  Surly Tuggnut. The Tuggnut is by far the easiest chain tensioner to use on the market, partially because it's the only that requires no tools. If your fenders are mounted on the outer side of the frame, the skewers are tightened against the fender brackets instead of tightened directly against the frame. You could avoid interfering with the wheel fastening solution by mounting the guards using P-clips on the seat stays. It is beter to adapt the mudgaurds than the frame. Horizontal dropouts require a more fixed axle to counter the  force pulling the wheel forward. QRs have a less firm grip, so chain tensioners can be used to prevent the axle being knocked out of alignment or sliding forward. Rather than adapting the bike to fit the mudguard, adapt the mudguards or use mudguards that attach to the seat stays.
Horizontal dropouts require a more fixed axle to counter the  force pulling the wheel forward. QRs have a less firm grip, so chain tensioners can be used to prevent the axle being knocked out of alignment or sliding forward. Rather than adapting the bike to fit the mudguard, adapt the mudguards or use mudguards that attach to the seat stays.