Brian, finding a true four-season, molded
fiberglass trailer with a $10K budget is going to be hard.
Bigfoot and
Oliver are the only manufacturers that offer the full package: thermal
windows, extra insulation, and enclosed, heated plumbing. All the others are three-season at best.
Pretty much any trailer with a
furnace is good down to the mid-thirties and, with some attention to plumbing, can withstand occasional dips into freezing temperatures. Any trailer can also be used dry (plumbing drained and winterized) as a winter shelter.
Bigfoots- the older three-season models- have a little more insulation than run-of-the-mill Scamps and Casitas and might be a better choice. But none of them are well-suited for extended below-freezing conditions. It'll be a constant battle to keep the plumbing going, and you'll burn through a lot of
propane. Condensation can also be a problem, leading to mold and rot.
You might also look at some non-molded options. They generally depreciate much faster so it might be possible to find a four-season unit within your budget.
But that raises the question: why a four-season trailer? How are you planning to use the trailer: when, where, and for how long? Isn't the whole point of a travel trailer to get out of winter?