Good move, going with winter tires on their own wheels.
FIRST...
There really is so little difference between those two tire widths(175mm or 185mm) in terms of, cutting through the deep STUFF. Either the 175mm or 185mm is too close to call as are any tires +/- just 10mm.
What I mean is for example, if your OE size width is 225mm then YES, dropping down to a 185mm or even 175mm, will make a larger difference than just dropping down 10mm to a 215mm wide tire. (I realize the FIT is not 225mm, I'm just saying!)
So yeah, you can go with either one but, it's mainly about, what do you want and how much money difference is there between the two tire sizes?
SECOND...
IMHO, the Honda FIT is already a loud vehicle on the road. Do you really want to introduce more noise(studs) into the cabin? Those studs are frikken LOUD!
You may in fact not need studded winter tires however, it is a nice option to have that can be done at a later time. So, I'm just throwing that out there.
Just adding a set of 4 winter tires alone to any vehicle is a MASSIVE improvement all by themselves and you'll love'em!
THIRD...
Should you get rid of/sell the FIT in the future, which size tires do you think might resell quicker, more easily as this could be important...Just say'in!
Good luck with your decision,
CB