Thanks Everyone for the responses.
To answer some of the questions above:
We are on the West slope of the North Cascade mountains in Washington State.
We have build a metal roofed cover that covers the entire trailer as well as the 8'x20' deck off of the front door. Not exactly a mud room but a covered space for wet shoes, coats etc.
We do quite a bit of grilling on the front deck to reduce cooking indoors. And, maybe, just because I like grilling
Our primary heat is portable electric heaters. We do have a propane forced air furnace that performs poorly as a backup. I do also have a propane catalytic heater but have not used it as it will add to my moisture problem.
We are working on skirting the trailer. We are trying to make it look proper and well done. We don't want to follow the example of the guy down the road that "skirted" his 1970's trailer with straw bales and blue tarps.....
The biggest real problem that I am seeing with the moisture in the trailer is not the windows but spaces like the bedroom closet and the mattress. The head of the mattress is tucked into a slide out so the top 18" is snugly surrounded by poorly insulated exterior walls. Also, it is a memory foam mattress so it does not breathe. Moisture that accumulates there has trouble evaporating.
It has warmed up a bit and I have moved the dehumidifier from the kitchen to the bedroom. With low temps back up in the mid to upper 30's we can keep the bedroom windows open at night. Between these changes the moisture trouble has been greatly reduced. I know, however, that if we don't take corrective action that the problem will return when it gets cold again.
I am interested in the heat recovery ventilator. I would expect that to be effective at reducing the "trapped" moisture in the trailer (and outbuilding) and likely much more energy efficient than the dehumidifier.