remember a skinnier tire "breaks through" the snow and ice better than a big fat foot print.. (which is why joked used a 215 tire in winter opposed to the 245s.) its common to see people use spare tires when racing (amature) on ice. spare tires are skinny and they bust through the snow. I'm *not* telling you to go get 4 spare-tires to ride on... ...
as for the smaller wheel (15") im sure he used that size simply because the tires were cheeper and easier to find.
Also, the driving school i attended (on multiple occations - MasterDrive) did a test on 3 different types of snow tires. 1 tire being a standard snow tire, 1 being a studded tire, and 1 being a "experiemental" tire with acorn shells chopped up into the rubber...
they found teh acorn shells performed poorly... they would shatter and chip away as soon as they met the ice. SOme pieces would simply fall out, leaving a large hole in the tread where a big chunk of nut-shell was.
they found with the studded tires the studs would get depressed into the rubber, thus shrinking the foot-print of the *usefull* tread. This makes them a un-needed cost, and in some states (Indiana) they are illegal to use.
They found the best stopping power to be in the standard snow tire.
They used an ice-arena as a testing ground.
I suggest Blizzacks (sp?) i suggest whatever size your car came with OEM.