I already have a truck with 10,000 lb towing capacity,
Towing capacity is only one part of the equation: Load carrying (payload, CCC, cargo capacity) is the other part. You will likely run out of load carrying capacity before towing capacity in most cases. A Travel Trailer will put between 10-12% of the GVWR
of the trailer on the hitch plus all the passengers, the trim level of the truck, and other stuff in the truck that can add up quickly. (A fifth wheel trailer, on the other hand, will put between 20-25% of its GVWR on the truck.)
The load capacity of a modern truck can usually be found on a sticker on the driver's door column, and it often has a yellow boarder or highlights. It reflects the capacity of YOUR specific truck as it left the factory. The published values in brochures etc. do not reflect values for your truck but usually shows what the the stripped down (base) model of that truck could have and it will be much higher than the real thing.
Very few trailers will have the cold weather capacity you desire for winters in the Chicago area. The Arctic Fox brand seems to be better than some but any trailer will require a lot of help. Double pane windows, sealed under belly, heated tanks, supplemental propane tank, skirted undersides, heated water lines all help but..... Be aware that many RV parks in the cold areas are not open in the winter, but a mobile home park might be. You might be better of looking at "destination trailers" for cold weather but.....
Try the "search" item in the menu line at the top of any page and look for something like "cold weather camping" ......