I've been doing tires part-time since the late 1980s.
The ideal scenario is to have a set of dedicated rims/tires for each driving season.
Every time I do a winter-summer changeover, I cringe because rebalancing requires that I remove all of the old weights and install new weights, and there is either a sliver of aluminum removed (hammer-on weights) or a bit of a sticky mess left behind (stick-on weights). Either way, the rim is "damaged" a bit and takes one step closer to being a POS.
And despite the "common knowledge" that aluminum rims are lighter, they aren't THAT much lighter to have any sort of real impact on gas mileage IMO, and steel rims are always more repairable. Steel rims can be sanded & spraypainted, impossible with aluminum. And if the rim is dented, 95% of steel rims can be hammered back into shape but I've seen very poor results when aluminum wheels are "straightened" after they hit a pothole.
For my car, it's steel wheels year-round.
With regards to FE. In my case, I only put snow tires on the front. It's impossible to judge whether this affects gas mileage, because there are other variables which also change at the same time- the air is colder, and the gas changes to a winter formula. So my winter gas mileage is always worse than my summer mileage, and it's possible that snow tires are part of that, but I can't really isolate it.
-BC
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