Not as many as you might think.
There are currently seven players on the 60-day IL (and 40 on the roster). So they're seven over the winter roster limit. But five of those 47 players will be free agents (Gibson, Syndergaard, Hand, Robertson, Knebel), and will come off the roster after the World Series.
After that, Zach Eflin has a mutual option, which he may decline. Nola and Segura have club options - Nola's will presumably be picked up, but Segura's may not.
Now, the club will want to make some space for serious minor league prospects who need to be protected from the Rule 5 draft. There are a lot of guys in the minors who will be Rule 5-eligible...but frankly, when I look at the list, not a lot jumps out at me as guys we can't afford to expose to the draft.
In the minors, the domestic rosters currently show a total of 197 players who aren't on the 40-man. They have to get that down to 190 in the off-season - but they'll lose many of the AAA players as "six year" minor league free agents after the World Series ends, so that really shouldn't be a problem either.
Bottom line - they may have to part ways with a couple of relievers on the 40-man (Damon Jones?), to free up space for a minor leaguer or two who they want to protect, but I don't see any need for large-scale purging (unless they just want to clear out some guys who aren't in their plans, of course).