Speak to your leadership about your work requirements.
In terms of environment, this continent is in early spring so there is always a chance of frost at night and cold nights that could conceivably get to 0C but not likely below that in Neverwinter. However, in places further north, there is still snow on the ground. North of the River Mirar which itself is a glacial river. Raven Rock may still have some snow or potential of snow for a few more weeks.
So I will treat you as warm blooded and therefore not going to freeze but may experience frostbite damage.
>naked
By the way, you didn't pass your clothes to Cat and it wouldn't go over well with the guards to have a onesie stuck to the bottom of the cart with a sticky fluid. So it was assumed you either gave your undergarments to Cat but forgot to mention it, or if you want to have even more fun, you dropped your undergarments on the other side of the now locked gate.
I'll leave it up to you as to what happened because I am a just and loving god kind DM.
Because you are warm blooded and susceptible to frostbite, wearing next to nothing will have the same effect as a human wearing next to nothing, so your rolls may start to have disadvantage if it gets cold.