Yeah, you shouldn't stop playing the winter event until you've got a gun, mortar, and frosted boots for each of your characters. Play with coats and scarves after if you like, but make sure you've got that much so that you can hit the ground running next year.
I've also been stockpiling things after that, should be able to buy anything new I want on day 1 of next winter event. Don't just burn your extras for scraps of latinum at the end of the event!
You should also keep running the daily race, even if you already got the ship. I've got my toons with a huge headstart on next year's ship, and started this year with about half of the needed pics. About half done on the summer event ship as well
As long as you've got a little room in your bank, definitely worth keeping this stuff, keeps you way ahead when the events launch. And from a money standpoint, you can sell your extras for big bucks when the event starts, people are always desperate for the new gear immediately, so the bells/beads were like 250-300k each when the winter event started...