I make this drive often - the 80/380/81/90 route is the best.
The only addendum I would make to the base route is to take I-690 in Syracuse to I-90, cuts about 5 miles off.
Now, there are some slightly alternate routes that will save you miles and tolls, but not necessarily time.
This one will put you through Ithaca and is a nice drive during the day this time of year (at night there are a lot of deer). It will also put you right next to Taughannok Falls outside Ithaca, which is actually taller than Niagara (though about 1/1000 the water flow) and past the old Seneca Army Depot which means you will almost certainly see the white deer.
This route is, much to the dismay of the locals, a short cut used by truckers, and one I use all the time. Again, at night there are a lot of deer, but it saves you 21 miles and some tolls. Almost the same time, though. The route is...OK. There's a small stretch that gives you a great view of Skaneatales Lake. Everything beats the thruway, though.
Anyway you take will also have tolls on I-290 between Buffalo and Niagara falls on the Grand Island bridge, also.
Regarding lake effect snow that time of year - the most worrisome area for you will be Syracuse. They have a band that sets up and just pounds them off of Lake Ontario. Otherwise, believe it or not, the NY Thruway route
for where you will be going is not too bad. Lake effect snows are wind direction dependent and very localized. I mentioned Syracuse already, when Rochester is getting pounded, it rarely extends down to the Thruway and has almost no effect on Buffalo. The only thing you need to watch is a strong SW wind which will bring the Lake Erie bands north and could really be a mess for about 20 miles near Batavia. But, the NYS thruway is extremely well maintained (at least as far as snow removal), so as long as you aren't in an "event", hit a rest stop for twenty if you get in the snow and wait for the plows to go through.