I would ... but you can also leave them outside in pots in a sheltered location and plant in the spring.

Sure, I usually divide my hostas this time of year and replant , or as esh said, leave in the garage or basement until spring. They go dormant so you can just leave them undivided and water once a week or so.

Hostas are a mainstay of my low-maintenance garden. Someone once gave me a hosta that was gorgeous but I had a baby and didn't get it planted. It sat outside and the potting soil got as hard and dry as cement. The hosta inside wilted away, and I gave it up for dead. But, being the procrastinator that I am, I left the pot for a while and watered it along with some other stuff. That hosta put out new eyes and came right back. It's sitting on my front steps right now, getting in some blooming before it goes dormant. It's absolutely gorgeous.

I've heard of hostas re-sprouting in the compost heap. So I think planting them now would be fine. (I just transplanted some and fully expect to see them in the spring.)