I put my beds to rest in the fall just by removing the remaining dead plants & weeds and then covering the bed with 2-4" of leaves or pine needles to prevent winter weed growth. If lime is needed I'll add it in the fall. In the Spring I'll either till in the rotting leaves or rake away the pine needles where the new rows will go in. The old pine needles are then used as mulch between the new rows.

I would do the same. I mulch all my beds for the winter as much as I can (depending on availability of materials). I often cut, say, asparagus fronds to mulch the tomato beds, and throw the tomato detritus in a back corner of my land. If I can get autumn leaves, those are sometimes mulch, or sometimes layered into compost.

The way you prepare a raised bed garden in the fall is no different that what you'd do for a non-raised bed garden. Having walls around soil doesn't really make gardening any different, except you might not be bending over as much to do it. Though a container, with walls lifted above soil, does require some extra care in watering.

Most of my beds are Huglekultur type that settle a few inches each year. As a disease precaution plants and fruit are removed to compost for later use in landscape beds. Native soil and partly finished compost is dug in to refill beds. Some are seeded with Hairy Vetch and weeds are allowed to grow in others. Growing weeds are turned under 2-3 weeks before planting. Weeds that flower before time to prep bed for planting are mowed or turned under to prevent going to seed.

Landscape beds are topped year round as needed with wood chip mulch.

I chop up residual remains and mulch up leaves finely and scatter them over the beds, Next I till them in. If I have a cover crop growing, I leave them alone.