You sure can! Ive been doing it for years. It can be as simple as putting your solar panel on top of your trailer and running the two wires to your 12 volt RV battery. Connect the solar panel wires to the posts of your RV battery with alligator clips.
I bought my trailer new and didn't want to touch the wiring so I did this for 10 years. Now that I'm retired I'll mount my panels to the roof of my trailer permanently and hard wire them into the battery leads but won't impact anything else in the trailer's wiring harness.
You can use an inverter to convert 12 volt DC to 110 AC but why bother? Inverters are inefficient and waste power. Your trailer runs on DC anyway. Any other items you want for your trailer are available in DC. This works great for boondocking
and if you visit a trailer resort the AC power will be provided if you need it.
The wiring harness in your trailer is a separate issue. It will be DC. One wire runs from the positive (live) terminal of your RV battery and the other from the negative (ground) terminal. These wires connect to a distribution box which should contain a fuse. If not, put an inline fuse in the positive wire from the battery. Individual lines should run from the distribution box through fuses to each fixture such as lights
, fan, furnace
etc. Each fixture will have a place to attach a positive wire, the runs that runs through a fuse in the distribution, and another connection for the ground wire which may or may not be a common connection at the distribution box. Some fixtures will have a built-in on/off switch. Otherwise you can add an on/off switch in the positive line from the distribution any place you want. Be careful not to mix up the positive and negative wires. Use LED bulbs in your lights
as they use 10% of the power used by the hot-wire incandescent types. Let me know if you have any questions.