I think in general, a shorter mowing height is probably appropriate in cool weather to prevent fungus buildup. You may need to take it a step down at a time, because IME that turf is very tough to cut the first time you lower the cutting height.

You're in a colder zone then here in Vegas but around here folks who do meticulous care with grasses that go dormant in winter will scalp them down as soon as they turn brown anyway. That may not be proper in colder zones, especially if snow that sits and remains for any period is expected, I just don't know. But around here scalping it down is proper proceedure.

I'm wondering though about you finding a need to lower a Snapper for leaf removal. I always raised the mower to the highest possible setting for the leaf removal season. I also set the engine rpm to idle. For me anyway, this worked great. In our dry climate the shredding of leaves will create a very dusty condition and running the engine at idle reduced the cloud. My situation may be totally incorrect for your conditions, just thinking out loud.