Rmack1,
You are getting lots of great suggestions here, but I can easily see a newcomer this getting a bit overwhelmed. The important things to keep in mind (IMO) is that you don't have to jump into doing everything all at once and that there is a wealth of help here available to give you a hand if you just ask.
I suggest you:
1 - Check, maintain, clean, test and/or (most likely) replace your battery(s). If you do replace, then by all means, use golf cart batteries (in series)....or AGM batteries. If you get more serious about winter camping, have in the back of your mind the future option of increasing your more battery capacity.
2 - As a minimum, use a digital volt meter to monitor your battery voltage when camping. Pianotuna posted a chart to help you with this.
3 - Change all lights to LED's. When I first made power use measurements and calculations, I found that the incandescent lights accounted for about 1/3 of my daily power consumption when cool weather camping (lows in the teens and highs in the 50's) winter (dark early) camping.
3 - Start thinking about a location (close to the battery if possible) for a replacement battery charger. I don't believe you need to go there just yet, but start thinking about it because it if very likely that you will wind up doing this if you continue winter boondocking. Yes, you could use a stand-alone charger outside the trailer, but who wants to fuss with battery connections at zero degrees. If/when you do put in this replacement charger, consider upgrading the wires to the battery to a heavier gauge (to reduce voltage drop) at the same time.
4 - Consider adding solar. I have yet to use my fancy (Honda) generator when camping...ever. I ran it once (when camping) for some friends to use, but usually our, non-solar, friends just plug their rigs into our outside outlet during the day to charge up. And for us, trailer camping season usually begins with the first snow fall (we usually sleep in a tent or just under the stars in the summer months).
Lastly, we all have put in some thought and time into these suggestions and I know that I for one (and I suspect I speak for others as well) would appreciate an update on your progress as you move forward with your project (mine took about $10,000 and two years to accomplish....on a brand new, "winter rated", trailer.
Have fun and enjoy the journey,
Steve