Can you still propagate cacti in winter?

I've already tried it and can tell you: in winter you need a lot more patience, but it definitely works. The real problem is heating air - it's often dry and warm at the same time, and cacti really don't like that. If you want to propagate cuttings or seeds, you should put them somewhere cool where it doesn't get above 15 degrees. Having heating nearby is your biggest enemy here.

With cuttings, I'd let the cut surface dry out for one to two weeks before you stick them in loose substrate. Water very sparingly - basically just enough to keep the soil slightly moist. Seeds germinate much more slowly at lower temperatures, it can take weeks before anything happens. If you have a choice, really wait until March or April, things move along much faster then. But if you have to propagate now, it works - you just need to water less and avoid the heat from the radiator.

If you want to try it, you mainly need stable conditions - and those are tricky in winter. The others are right that it goes slower, but the bigger problem is really the combination of dry heating air and low natural light. Cacti really don't like it when everything's working against them at once.

My tip: If you want to propagate now in August, do it instead. You've still got a couple months before things really get critical. In winter it's barely worth the effort - I'd just store the cuttings dry and start again in spring. You'll save yourself frustration and have better odds.