Do you have an electric or gas powered leaf blower? Hose off the table and blow it dry using the leaf blower. It's a trick I learned years ago to help with washing the road salt off the car. Thank goodness in Florida I don't do that anymore. :)

I think it depends on the style of the banquette. If it's a relatively open banquette, say, with the banquette only on one side of the table and lots of room on either end to get in and out, then legs would be fine. But if it's an L-shaped banquette or there's not a lot of room where you would enter or exit it, then you definitely want to do a pedestal. I know the way my banquette is set up there's no way a table with legs would work.

Hmmm-- sounds like your woodworker needs a different lumber yard. There's no way I would invest the time and money in building a custom table without picking the right boards for the project. There's too much variation from tree to tree to trust a tabletop to chance. There are plenty of places that will sell you whatever you need in any species you want, providing pictures of the actual boards if you don't have a better local source. I've linked one of my favorite fantasy wood sites below. That said, there's nothing wrong with a veneered top, especially if you want a burl or bookmatched top. I do tons of stuff with birdseye and curly maple in cherry frames, so I'm not unbiased' but I think its a great look that worked 300 years ago and will still work 300 years from now, "dated" though it may be (not sure to what date though, its been used for a long time). Coming up with a pleasing symmetrical layout for an odd shape is certainly more challenging than doing it for a simple rectangle or circle, but certainly not impossible and perhaps much more interesting. Take pictures of wood you like, like the one above, print them out and start cutting and folding to try different layouts. Flip the pictures before printing to make bookmatched pairs. Here is a link that might be useful: wood porn

I'd get all the snow and moisture off and leave it exposed as long as the days are clear. Then I'd cover it with an absorbent material (old sheets/towels) and then cover that layer with some heavy plastic sheeting or a tarp. If the base is made of the same material, try to keep it protected also. Remove the plastic every few days and dry or replace the absorbent layer. If you don't have a long, hard freeze you'll probably be OK. I would avoid the hair dryer since heating one area too long while the other may be frozen could cause more damage then just leaving it alone. If the weather stays nice for a few days, you could set up an electric fan so that the air blows across the table. Afterward, cover it again.