On the 06' the tire pressure sensor is a passive sensor, and is based on the ABS. If the ABS is acting up, that could be part of your issue.
We average 108" of snow where I live here at the PA/NY border. (Anchorage averages 75" by comparison) I have run Blizzak's and General Atlimax Arctics with really good success with vast quantities of snow on the road, as well as some icy conditions. Hands down, two of the top winter tires on the market. I do not use studs, as I like to use my snow tires to pass inspection in the summer time.
Otherwise, what Bookworm suggested is solid. Some added weight over the rear end could help vastly.