Do you have a fuel tank?
That will be your obstacle.
Your looking at a bit of work. There is room in the frame to run water lines to the garage, and I would add an additional outlet tor the washer. I added a 20 amp circuit in the garage for a variety of reasons, but mostly to be able to safely run a small heater. There is room in the panel box for additional breakers.
The hardest part will be adding the washer drain. There is minimum room under the floor with the fuel tank there to run plumbing.
I have MOR/ryde IS under my traielr, so I can't get to my rear grey tank easily.
If you can't get to yours - you could tee into the the rear grey tank drain under the trailer. Then use one of the gate valves on the main sewer drain to close off the 3" pipe. If you keep the rear tank drain open you will then have storage for the washer use. Or you have to be diligent and keep the main drain open whenever you use the washer - which is how some trailer manufacturers install them.
We use our W/D a lot, it would take up way too much room in the already small garage. W/D stays in the front closet for us. If not washing, the shower towels always go in the dryer for 20 minutes.