The Big Mac Bridge closes more often now then it used to, due to some folks that managed to drive over the railing. The Bridge Authority is tired of being sued, so they close it now. I went north for gun season and the bridge was closed for several hours with lots of gun hunters waiting to cross, and that was just for winds gusting in the 50 to 60 mph range. Hopefully things will calm down abit prior to your arrival. Just an FYI, many of the hotel/motels close in Mackinaw City for the winter, so a room could be hard to get if needed, and Gaylord is pretty much the last town to get lodging at, and with it being snowmobile season they could be tough to find there too.
With a possibility of snow and blowing snow, you may want to plan on a longer drive time, maybe much longer, if the lake effect snow's kick in with the cold air moving in you could have some tough driving from Grayling north and then parts of the UP could be getting more snow too. And with the temps as cold as there going to get, the roads will probably remain snow covered and tricky for awhile.
If the bridge is open and you have gas, there's no reason not to go over to St Ignace, there are plenty of gas stations on US 2 just west of I-75 (provided your using US2), I just find getting off at Mackinaw City a pain as the exit and on ramps are kinda of a pain and the stations while close, may have you driving around an unfamilar town to get back on the freeway. There's also some fast food, but they'll probably be closed by the time you make it there. There is a truck stop, not sure if they have food 24/7 or not but they'll be open, as the Shell and Holiday gas stations are normally open 24 hours.
After Mack City/St Ignace, fuel will be hard to come by if traveling late at night, until you make it to Munising. There's a Mobil along hwy 117 near Engadine that usually is open, and stations in Newberry on US28 east of 117 may be open late at night.
Good luck.