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.