You should wait on a clearer day with not much frost or rain as these will make mowing extremely difficult to do neatly and uniformly and you will probably need to clear some leaves before you can start and the ground will probably be soft but leaving the lawn for a long time then mowing it all at once is bad practice and can look untidy so if you keep it up it will look a lot better coming back into spring for it.
You should also consider raising the setting for the lawn mower by a setting and be careful not to walk over the grass or let anyone else over the grass too much when its frosty or you could leave footprints where the tips of the grass have been snapped off.
Its a really good idea to mow your lawn a week or so before Christmas or new years to make it look substantially tidier for the holidays when family or friends visit and can really lift a winterized garden.
Definitely do not scarify your lawn unless there's a good chance of natural recovery as the lawn will go white and horrible if it goes frosty after scarifying and moss could grow in bare areas by spring time which is odd as some companies still do this into winter and they're supposed to be the experts. There are a lot of advantages to mowing and keeping a tidy lawn in the winter such as it helps keep pests away such as mice and insects and other damaging pests and it will look a lot better.