I also reside in Michigan and have stored my TT's outside for decades without a cover.....no problems.
Most of the TT's, HTT's, FW's, etc., where I store my TT outside are un-covered, but the ones that are covered you can sure tell the quality covers from the ones that aren't. So if you buy a cover, pay the extra for quality, they seem to fit better, panels don't blow in the wind, and they last longer.
With or without a cover, check your HTT throughly twice a year for any caulking issues on the roof and outer sidewalls (seams, windows, vents, etc.). I also found when in storage keeping my TT at a slight angle (nose up in my case) minimizes any standing water and helps with snow/ice melt-off.
Bob
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2016 GM 2500HD 6.0L/4.10
2018 Jay Flight 24RBS
2002 GM 2500HD 6.0L/4:10 (retired)
2005 Jayco Eagle 278FBS (retired)
1999 Jayco Eagle 246FB (retired)
Reese HP Dual Cam (Strait-Line)