They say not to disturb them once planted but if you really need to split them probably early Spring would be best, but I'm sure someone else will have more definite advice for you

I split a pasque flower last week, accidentally but as the ground is still warm it should settle water well if no rain though.

which anemone? if it is the Japanese ones then spring is a good time.

Sorry, but disturbing an established plant is a death sentence for it. Even small plants resent having their roots damaged as they are when moving them.
Having said that, they can be propagated from root cuttings, but doing so is very risky and involves the death of the parent plant.

I transplanted a Pasque Flower into a pot before moving house then replanted it in the new garden. It's doing well.

Transplanting a whole plant with little root damage is not the same as taking a clump and splitting it up into smaller plants.
Even so I stand by the dangers of moving them. I grow hundreds of them for sale each year.

My 'splits' are starting to look a little sad so I do hope it will perk up.

Why not save the seeds next year? I have to admit that I saved them last year and only a few germinated but still a sense of achievement.

Thank you for all your replies. I definitely won't be splitting them up but I might try removing one plant, disturbing the roots as little as possible. The problem is I have a white one & a purple one now growing really close together. I didn't realise how much they'd spread when I first planted
them some years ago.

Seed should be sown when fresh and only the plump ones at that. A lot of the ones in a seed head are infertile.I tend to nip off the 'tail' too as these can rot and kill off the seed, though that is just personal preference.
Germination may be straight away or in Spring. They do not need any heat, only protection from excess moisture.