when is a good time to scarify the grass?

I don't think so - my book/s tell me that you need to cut the grass three days before you scarify, then again the day before, to get deep into the 'thatch'. So mid-winter can't be a good time, can it?

I don't think it would hurt the grass to do it in the spring, although I'm no expert on grass care!

I always scarify in the Autumn and Spring. You should really have done it as soon as the moss went brown in the Autumn. Now you must wait for a dry day in the spring.

Don't put the moss on the compost heap as it will get spread round the garden.