Probably not.
Carrots naturally (or due to selective breeding) come in an extremely wide variety of colors from white to yellow to orange to red/pink to purple.
It's likely that you were simply looking at two different varieties, one of which was more pale than the other.
click image for source Even the color being only "skin deep" isn't necessarily a sign of it being a dye as many carrots have white cores, or at least cores that are more white than their surrounding flesh.
Which you can see an example of below:
cooking.stackexchange.com/users/33128/Catija
It's probably not anything so sinister.
Even typical orange carrots do vary somewhat in hue.
And as with many other vegetables, "heirloom" varieties of carrot have started to make a bit of a comeback in the US.
As you can see here there's a wide variation in color among these heirloom versions; they can range from very pale, almost white to brilliant orange to a deep purple.
cooking.stackexchange.com/users/25059/logophobe
The other answers did not mention the packaging.
Carrots that come in bags (like baby carrots) often have an orange grid pattern painted on the bag.
This makes the carrots look significantly more orange than their non-bagged counterparts.
cooking.stackexchange.com/users/44835/Timothy Kanski
Carrots come in lots of colors from pure white, yellow, orange up to and even including deep purple.
They are not dyed.
cooking.stackexchange.com/users/33134/Escoce
Carrots are not dyed, but they are orange because of a substance ( Carotene C 40 H x ) in them that is actually named after carrots.
Many other orange foods get their orange color from Carotene.
cooking.stackexchange.com/users/44838/n00b
In response to your question, carrots are not dyed.
(Unless of course you are talking about the mini frosting carrots on carrot cakes)
Regular carrots, however contain a natural pigment known as carotene which is also found in humans to some degree.
This carotene is naturally orange leading to the color of carrots.
Technically speaking, if you ingest enough carrots, or any other food such as tomatoes rich in beta-carotene, you will take on a slight orange color in a condition called Carotenemia.
cooking.stackexchange.com/users/44945/B00sTMe15TeR
I was in the supermarket and I noticed that one brand of "organic" carrots was a very pale orange, but another brand of carrots was bright orange.  Is this color difference because the carrots are being dyed?
Are carrots dyed orange?
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<vegetables><carrots><coloring>
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cooking.stackexchange.com/users/26201/Drisheen Colcannon
The carrots are probably not dyed, but rather contain a substance called Carotene C 40 H x. Carrots can vary in colour from white to deep purple, but even regular orange carrots will naturally have different shades. Carrots are not dyed their orange color is a result of carotene. They also come in other colours.
Carrots are not dyed. Carrots come in many colors. The orange ones are orange because of carotene. The shade of orange varies greatly.