Decomposition can and does happen all winter long. I had piles 4-6' high of tree chips and steam rolls off these piles causing fun, moody halloween effects all winter long. Dig down a few inches and you can start feeling the heat. Decomposition releases a lot of energy. In the spring, I kid you not, these 4-6' mounds were 6" high and the blackberries I covered were GONE.
Your decomposer, however, is small. You could and should be adding nitrogen to the mix. The nitrogen is important to 'feed' the decomposers. They use lots of nitrogen to do their work. There used to be cat litter made exclusively of alfalfa. Little pellets of super nitrogen, super 'organic' and cheap! That will help raise the temperature of your compost and make the process faster!
I would go ahead and use my compost at 90% done to cover the beds now! What is left to be decomposed will continue to decompose no matter what. The second something dies that something starts decomposing. Definitely slower in the winter but these decomposers are like hefty construction workers. Gotta feed them well (nitrogen) to keep them 'pooping'...sorta kinda. That's how I like to think of the process, grins!
You could also try growing a 'cover crop' for the winter. There is not that much mulch for a single bed. Depending on the size of your bed (mine are at least 3' wide and a good foot to a foot and 1/2 high and I use at least 4 to 5 cubic feet, 2" thick per bed.
The seeds you can buy in bulk cheaply, are 4 or 5 different choices of leafy, hardy, annual plants. Depending where you live, you will have a dark green reversed 'grave yard' where the graves are dark green and the walkways are whatever. If you don't have raised beds we should talk about that later. I'm not talking about any lumber, bricks for sides!
This cover crop is cheap to buy as seed; buckwheat and annual rye are my favs. Do a mono crop per bed if you want to try out different crops. That annual rye grew 2+ feet (a tall, sturdy grass), talk about looking weird in winter!
Buckwheat is a pretty plant and the easiest to chop up and turn over in the spring. The zone I was in at the time was 4-5 USDA. In the early spring as early as the soil can easily be worked, one just takes a shovel and turns the whole kitandkaboodle over, chop it up a bit, add some nitrogen and in a few weeks to a month that bed is ready for planting the season's crop. Talk about a LIVE soil! 'it's alive, it's ALIVE'!!!
I think I've got Halloween on the mind...I am being weirder than usual, grins!!