I mean, if you rarely check the pressure of your tires or store your car and leave it sit for a long time, than it does have a positive impact. But otherwise if you get your tires filled at a shop that has a good industrial air compressor with dryers, the benefits of no moisture in nitrogen are moot.
Even with dryers, moisture still gets in and also air is affected by temperature. Since we live in an area where it can be 30* at night and 70* during the daytime, nitrogen isn't a bad thing. Even a little bit of moisture gets in and the drastic temp changes will cause condensation.
Air presssure changes with temp by about 1psi per 10* so if you fill your tire in the afternoon, You would be about 4 psi lower at night. Also note that driving long distances or high speeds raises the tire temps as well.
Yes I do have a car I store over the winter.
As for cost, The shop that puts on tires for my cars fills them up with nitrogen with the pruchase of the tires. So since they do it with a purchase, It doesn't hurt to have them filled. If I recall they only charge $5 per tire to purge/fill with nitrogen if you already have tires on your car.