Power to trailer

Go to a good marine shop and pick up an on board boat battery charger plug. It will be a "male" plug. It will go through the trailer wall and then can be tied into the trailer inside 110 v wiring. You may have to ad that along with plugs. The extension cord from the generator can then be plugged in out side the trailer for inside trailer power. The trailer can also then be powered from onsite RV power with an adaptor or from any house 110 v current supply. I have done this on several trailers and it is the best set up I have found over the years. Also the exterior plug comes with a rubber cap to seal out rain.
I know they are available at Bass Pro and others.
Here is a link....https://www.basspro.com/shop/en/promariner-pro-tournament-ac-plug-holder

Paw Paw

Could you just use a small camping propane heater? Assuming you have a vent in the trailer...may want a CO2 monitor as well.

You may check into a good quality air mattress with a good R# insulation rating.

Do you really want to be that guy running a generator all night? Try this.

https://www.amazon.com/Mr-Heater-F274830-Indoor-Safe-Portable/dp/B01DD6…

What Paw Paw said then get a 110v electric baseboard heater. Little chance of catching fire, no fumes and will keep you comfy down into the 30deg range.

Here is what I did.

Order one of these. Drill the hole through the front wall of the trailer (I believe it's 1 7/8 inches). Grab any decent power strip, cut the male end off, strip the wires back a bit and wire it directly to the inlet plug linked above. Now you have a pass through. I can take pics of mine later if you still need more clarification.

The other option if you just want to run lights and charge a phone is a deep cycle battery on the tongue. I have one of those also and it's wired to an inverter on the inside for AC power. I also ran a wire from the light switch directly to the battery (with an inline fuse) so the interior lights work by themselves. To charge it, you can wire a tender in, mount it on the inside of the trailer, plug it into the power strip and when you get home you just plug the trailer in and the tender starts doing its job.

Silicone whatever holes you drill. Trailers love to leak in my experience.

I have had one of these and they use a lot of fuel.
Also, I know they saw they are safe for indoor use, but if you have ever had CM poisoning you will not want to take the change. Stay with electric heat in that enclosed small space.

Paw Paw

Get yourself a KICK ASS sleeping bag and you won't care about the temperature in the trailer.

I can't tell you how much happier I am since I got one as a birthday present many years ago. Seriously, it's a game changer. Many more like this one, I'm sure:

https://www.rei.com/product/896030/kelty-cosmic-down-0-sleeping-bag

Expensive, but worth every penny.