I thought snow tires used a softer compound with more aggressive treading, but that maybe an old school concept. Things generally get better over time. I've never had the need for snow tires though.
Unfortunately for those in the US, we don't have easy access to tire rolling resistance ratings.
Another simple thing to try in addition to the grill block is to remove the 'snorkel' connecting the air box to outside air for a simple warm air intake. It can be taken further by using ducting to collect air from around the exhaust manifold or other hot spot.
Back when I had the HHR, I put insulation around the engine block,
I don't get much play with the snorkel on this car. Though I could probably just remove it. The bigger problem is that the car has no lower engine cover, and with the bumper bein in the shape it's in, I don't think one could again be safely mounted. Unless I could drag one out of a junkyard <$20, I'm not sure if like to spend the money on this car anyway.