Dolomites in Early December

I am somewhat perplexed as in Alpine countries you can have hikes in summer and hikes on the snow in winter. As for intermediate seasons, you never know when exactly Autumn breaks, when snow arrives in winter and when snow melts in spring. But December is very very late, it maybe time to wait for snow (more likely in these climate change times) or maybe snow may already be there. Cable cars open for skying, but if the snow is still to come, early December may be a very damp and grey weather time.
How damp and how grey? In this very moment the top temperature in Ortisei is 9 °C (48 °F). Next weekend, top temperature will be 3 °C (37 °F) and could already get lower and snow a bit in the night. - When you have really a lot of snow, Alpine resorts turn alive again for winter sports (but in this case you will need snowshoes even for hiking).

Even though I do not live in Italy, I too am a bit perplexed as you seem to think the lifts
run mainly in summer, and you think the towns that are ski havens will be deserted in
winter...

There will usually be a break in the lift schedule during the fall for maintenance. But by
December (and when in December may be relevant), the lifts will open again for skiing,
and for hikers. Especially in the Alpe di Siusi. Given the climate situation these days,
whether the lifts will open if there is no snow is a question.

Getting around mountain towns is not that easy, and will probably take a half day door-
to-door. If your goal is to maximize your time, I'd stick to one place. As for which one,
Cortina is going to be more pricey in general. But in the Ortisei area, you have the option
of staying in the town, or in a property in the Alpe de Siusi itself. For your stated objective,
that is what I would aim for. The paths are not steep or technical, and for the most part
you probably need nothing more than nice hiking boots and poles to enjoy.

Finally, you might want to move your post from General Europe to Italy.

I'd stay with one base in Val Gardena, and the timing piece that matters most is that the big lift systems usually open together for ski season in late November or the first days of December, so after opening you'll find lifts running and many huts serving lunch, though your hikes become winter walks on groomed or snowy paths (worth checking this year's opening date before you book). From planning a lot of December trips in the Alps, the thing people don't expect is the Dec 8 holiday weekend, when much of northern Italy heads to the mountains, so book lodging and any special dinners early if you overlap it. The real bonus of December is the South Tyrol Christmas markets: Bolzano, Bressanone and Merano are an easy day out from Ortisei and mix Alpine and Italian traditions beautifully, so look for speck, apple fritters and the dense fruit bread called zelten alongside the mulled wine. Venice in December is then wonderfully quiet and atmospheric; just pack shoes you won't mind getting wet in case of high water. Happy to answer anything else here as your plans come together.

In the Val Gardena you have the choice of staying in Ortisei, St. Christina or Selva, all close to each other. The Christmas markets are a big bonus… these are easy from the Val Gardena… Chiusa/Klausen, Bolzano/Bozen, Bressanone/Brixen and the Val Gardena itself.

https://www.klausen.it/en/enjoyment-region/klausen/events/christmas-village-klausen.html

https://www.dolomiti.it/en/bolzano/events/christmas-market-in-bolzano

https://www.brixen.org/weihnachten/christmas/

https://www.valgardena.it/en/winter-holidays-dolomites/events-highlights/christmas-valley-in-the-dolomites/

Here is some further information.
The lifts open for the ski season on 4 December.
https://www.valgardena.it/en/news-val-gardena/detail/winter-opening-in-val-gardena/

The virtual map in the link shows possible winter walking routes in the Val Gardena valley.
https://dolomites-val-gardena-inverno.digimap.virtualalps.info/en