It does not get cold in Copenhagen in November.
It has a maritime climate and
the average daytime temperature in November is +7.1°C
(24-hour average +5.1°C).
The record low for November is -7°C, which is still no problem for cycling with a hat and gloves.
You do not need any special bicycle or special outdoor gear apart from normal layers for a mild winter.
It should certainly be possible to rent a bicycle in November.
Some outlets may be closed as it's a low season, so you should contact rental agencies in advance.
travel.stackexchange.com/users/2509/gerrit
I live in Copenhagen and use my bike to go to work all year like many other locals.
There are plenty of bike rentals for tourists as this is a popular way to explore the city.
You will find that the scenic city centre and waterfront a best travelled by foot or by bike as car traffic is restricted.
Its is a very good city for cycling with high priority to bicycle and foot traffic and bike lanes everywhere.
If there is snow in the winter the bike lanes in the main roads are cleaned quite quickly by the municipality.
November weather is normally nice, but some rain and wind is likely.
Snow is unlikely.
Bringing gloves is probably a good idea.
That time of year I would also recommend bringing a light poncho or raincoat just in case.
Please be note that you can bring your bicycle on the S-trains and Metro so you can combine the door-to-door flexibility and ubiquitous free parking possibilities of the bicycle with public transport for longer distances.
It is free to bring a bike on the S-train: in the Metro you need an extra ticket and there are certain restrictions during rush hour traffic.
travel.stackexchange.com/users/36506/mjul
We currently have mild weather in Copenhagen and it should stay that way for the coming month too, although you may see snow and sleet eventually.
That should not be a big problem, given the correct clothes, as stated by others.
As for bikes, check this out: http://bycyklen.dk/en
travel.stackexchange.com/users/36494/Dan K
As far as I remember people cycle all year long.
Maybe when it snows a bit less people do it due to ice.
Relating to renting, the city used to have a free public bike system.
The problem sometimes is more to find a bike available.
travel.stackexchange.com/users/3736/nsn
While there are many good answers, I think there is a big point being missed here: the great unpredictability of Danish weather .
Contrary to what another answer claims, the temperature can go way lower than -7.
For instance, the Danish extreme for November is just below -21 degrees Celcius (and there's not much difference across the relatively small country).
Also, autumn/early winter is the season for storms in Denmark , which (on its own, cold or warm) may make it very impleasant and/or dangerous to go outside.
My point: you should be able to rent a bike and explore the city, but beware that in November the Danish weather can vary a lot, so check the forecast before you go, and maybe have a plan B ready.
travel.stackexchange.com/users/36512/Henrik Christensen
Yes it is quite common, there is actually a lot of tourism in relation to bike tours, walking tours and boat canal tours.
For instance Nova Fairy Tales (former Copenhagen Fairy Tales) has a pretty good bike tour in CPH .
Regarding time of the year, I think you should be fine in November as long as you wear warm clothes.
It's mostly in the period of December to February, that it can happen to snow.
You'll see a lot of natives bike even in these period, so I'm sure you can still enjoy a bike tour in November.
travel.stackexchange.com/users/65802/Dave
I've a trip planned to Copenhagen in late November, is it fairly common for people to rent a bike and explore the city? I'm specifically asking as I'm not sure about people riding a bike in November as it tends to get cold early in that part of the world.
Renting bikes in Copenhagen
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travel.stackexchange.com/users/8534/edocetirwi
It does not get very cold in Copenhagen in November, and while some bike rentals may be closed for low season, you should not need a special bike or special clothes beyond gloves and a raincoat. People cycle all year round, and bike lanes are cleared of snow quite quickly. It is free to bring a bike on the S-train, but in the Metro you need an extra ticket and there are certain restrictions during rush hour traffic. Temperatures in Copenhagen in November can be as low as  -7°C, so warm clothing and gloves are recommended for cycling. However, locals cycle all year so it is possible to enjoy a bike holiday in November. Moreover Cpenhagen is a very bike-friendly city. There are plenty of places to rent bikes, many bike lanes and bikes can be taken for free on public transport. 
There is some debate as to whether the weather in Copenhagen in November should be classed as cold or not. It may reach  -7°C. However, locals cycle all year round so it is possible. Some warm clothing and gloves are recommended. Maybe keep an eye on the weather forecast and have a plan B. There are plenty of places to rent a bike and Copenhagen is a very bike-friendly city with lots of bike lanes. You can also transport your bike for free on public transport.