The problem isn't just the moisture on the windows. There may be 'sweating' going on inside cupboards and closets on outside walls. And there can be moisture forming on the floor, inside or below the carpet.
Moisture in a trailer or MH is a real problem in cold weather. I think a dehumidifier is a very good idea. It also helps out in the other seasons, especially in the Spring on those warm but very humid days.
But opening up cupboard doors and circulating air to warm outside walls and ceiling/floor surfaces can help: if you get the surfaces above the dew point, then moisture won't condense.