Well, this is a bit of a pain because the Model 3 Performance has really big brake calipers so that you can't fit the aero wheel 18" that comes with the normal Model 3. That's a bummer because the wheel covers give you almost 5% more range (and every little bit counts with a car like this). In China, they actually have a 19" aero wheel, but you can't get that in the US.
Now you can actually get these 19” Aeros for $3K directly from Tesla. That’s a nice choice and this is installed.
But if you want to go the DIY route, Fastwheels and Ian Pavelco have developed a really nice wheel called the EV01+. This has wheel covers too and in tests, it has nearly the same efficiency, so off to get those.
The problem is that they don't distribution in the US, so there is only one online retailer that sells these wheels called https://canadawheels.ca however they only stock the generic EV01 which don't come with wheel covers.
There is a whole list of EV01+ on their site, but none are in stock.
By a careful comparison of the many (and confusing) specs for wheels, it looks like the EV01(+) that is SKU W162164 (the manufacturers part number is FE01N(+)-1880-65TN+38C661) is 18x8 (this is the wheel diameter and the width of the rim), has a 5x114.3 bolt pattern (that is 5 bolts on 114.3mm centers and an offset of 38mm and a bore of 68mm is the correct one for $228 each.
As an aside, the model 3 has a maximum offset of 40mm, so this will fit.
The set that is identical but without the wheel covers is W162167
Now what tires to get, well one confusing thing is that the 245/45R18 tires that are needed for this size. This means 245mm wide and the aspect ratio is 45% so that the height is 45% of the width and these are 18-inch rims.
These will actually fit either 18x8 or 18x8.5 inch rims, so the above are 18x8, but you can fit others.
Finally, because the car is heavy, you need something that is XL rated. Confuse yet?
Looking on the forums, the choices seem to be the highly rated Michelin X-Ice xi3. This is a true studless Ice and Snow tire, so you want it for really wet and heavy snow conditions.
You can also get a special Tesla version of the Pirelli Sottozero 3 that has noise deadening inside of it. Tesla tires typically have foam inside, because without the noisy gas engine, the road noise is really evident. Doesn't grip as well but should be quieter. This is not a dedicated snow tire, but a Performance Winter/Snow Tire. In their tests, it does better on dry and wet conditions and is decent in snow with the Michelin Pilot Alpin PA4 coming in first, but the Pirelli (and the Dunlop SP Winter Sport 4D) close behind.
The place to check for these is Tirerack. And as an aside, if you buy from there, you can get the TPMS sensors and have them delivered to a local installer. You will still have to take the wheels down to them, but it saves some trouble.