You have no alternative except to monitor the National Park Service road conditions and restrictions reports, e.g.
https://www.nps.gov/yell/planyourvisit/conditions.htm . I'd also check with the rental car company to find out if they allow snow chains, and if they do, get some. If they don't, then be aware that any damage incurred using them will be on your nickel; any insurance (and other contract terms?) will be voided.
Twelve hours a day is fine, however three or four of them are going to be in the dark; not my preference if it's dark
and snowing/raining.
Route comments: I would drop Glacier as it's a giant detour and the GTTS road is already closed. So is the North Cascades Highway, the only access to NCNP. Only the low elevation roads are open in Mount Rainier NP; the road to Paradise requires chains.
Olympic NP needs at least two full days to experience; the Hurricane Ridge road is currently open but day to day, and they check for snow chains before letting you on it.
One thing to bear in mind is that it's not just snow and ice that can spoil things; it's also cloudy and wet weather. For example, with Mt. Rainier, except on sunny days (rare at this time of year) you simply can't see the mountain, period. Not even from the Paradise visitor center, if you could even get there. I just checked Grand Teton, and same thing there - 21F, snowing, and the mountains are totally obscured by clouds. Long way to drive to see bupkis.
Given all these limitations let me ask a dumb question. Why don't you plan a different trip? For example, fly to Portland, get a car, visit the waterfalls and vista points on the historic Columbia Gorge Highway, visit Timberline Lodge on Mount Hood, so you've got your volcano. Then follow the Columbia down to its (awesome) mouth at Cape Disappointment, fabulous if it's stormy, then up the Pacific coast to Lake Quinault, Ruby Beach, and the Hoh rain forest, all at sea level thus exempt from snow. The Hoh rain forest is magical in the winter - google "Hall of Mosses trail." Visit more incredible rocky beaches at La Push, then head around the top of the Olympic Peninsula to Port Townsend, ferry to Whidbey Island, then down to the Mukilteo ferry. Visit the Boeing factory in Everett, then Seattle, then end back at PDX. Map -
https://goo.gl/maps/CrPk5EMX8dT2
All just a thought experiment, of course; but I think your present plans are largely unrealistic.