You can add coffee grounds to a compost pile anytime you have them to add. When to put them on your turf grass depends on where you are in the United States. Up here now would not be a good time to apply coffee grounds since the
Soil Food Web is slowing down due to the cooling of the soil, although there is still strong evidence of very active earthworms (moles and castings) appearing in the yard and earthworm activity means Soil Food Web activity. Some parts of zone 6 might have soil warm enough for the SFW to digest coffee grounds and convert them to plant food for the grass to store.

last winter i collected tons of UCG and just would continually spread them on the lawn all later fall until the spring. I was even spreading it on top of snow on some days. I was able to cover the whole front lawn over that period with a good amount. I figured it couldn't hurt, even if it wasn't going to decompose until the spring.

Also... a few years before i had collected a tons of leaves from the neighbors and just added all the UCG to the pile. I would even turn the pile every few weeks through the fall/winter. It was always cooking the leaves and steaming when i would turn the pile. I would have to take off my coat and jacket just so i wouldn't get too hot from all the heat it would give off. It did smell like an old ash tray...
but by the time spring rolled around, i had great compost.

If you can get it, and don't want to use it in the cold, then yes, compost it. Otherwise I would never compost something as fertile as UCG. Use it as a mulch around plants.

just be careful to not mulch too thick... it quickly becomes a solid dry block and is water repelling.

That's the problem. I had access to quite a bit of UCG this past Summer and I ran out of uses for them. They really cake up if you put on too thick a layer.

Wish I had a source on over roasted beans, that I would like to try for a mulch.

i only had the caking issue when i used in on the perennial beds... all the UCG that i spread on the lawn disappeared by early spring without any issues.