We drove through the snow, reasonably thick although somewhat plowed but still driving on a good layer of snow and while snowing, in Flagstaff, Arizona 15,000' above sea level, during Christmas of 2019-2020 where there's also snowboarding/skiing and we got by fine. Just like the previous poster we simply drove slower and took it easy. People with lifted trucks were driving like crazy and stuck in the snow, not realizing their idiocy for driving fast.
We had all-season tires equipped at the time and they were Bridgestone Dueler Alenza Plus from Costco. They were okay but bump-absorption during non-snow driving could've been better, although a lil smoother on bumps than Continentals.
Keep in mind my Odyssey came with 17" wheels, not 18" So my tire size is slightly girthier (thicker sidewall at i think 65) Im glad i don't have 18", The ride quality on my Odyssey isn't smooth enough to go that low IMHO. The Toyota Sienna maybe, but the Odyssey, meh. Then again the newer generations could be different and i haven't rode in one that new.
Our previous minivan was a 2000 Oldsmobile Silohette, had i think 16" wheels, rode smoother, got better gas mileage, factory privacy glass (just like the Sienna), and had more power. And i think it had Goodyear tires on it, too.
A previous poster said Costco's exclusive Michelin X's are the same as the Michelin Defender's LTX for cheaper but i disagree. They're different tires, have slightly different tred design, so idk why one would think they'd label two different tires if they're the same.
That being said, my brother has X's mounted on his 2016 Toyota Sequoia 4x4 black limited edition (which would be excellent for the snow) and they seem to work great on dry road, although he's only had the car for a year or two.
My recommendation is checkout TireRack.com they have a tire shopping assist tool and they do real-world testing with recorded data and specs, more specs than Discount Tire or Costco give you. As far as research, but as far as purchasing, you can purchase from whoever you like.