Sounds like your current helmet doesn't fit you. You really shouldn't be able to push it around your head so easily. A helmet should fit very snuggly.

Go to a bicycle shop and try on a bunch of helmets. They do fit differently. I've got one I picked up fairly inexpensively because I cracked my helmet on a ride and quickly needed a replacement. It seems rounder inside than all my other helmets, so I wear it as a winter helmet with headbands and balaclavas inside. My Bell, on the other hand, is narrower and fits my head quite snuggly.

I've cycled in temps down to -40C in Winnipeg and have never had a helmet problem. My computer has gone black in the cold, and I've had trouble with shifting, but at -40 ... I don't blame the bicycle for not wanting to work properly. You could have probably superglued the velcro back on.

Yes, the lights fit onto pretty much any helmet, and so do the helmet covers. But if you want a really inexpensive helmet cover, you could just go with a shower cap ... lots of people go that route.

You might check REI and see what they've got. They are probably the closest thing the US has to an MEC.

I've had several Bell helmets ... I have found they work well for me. Other people like the Giro style ... they seem to work well for them. Others like other brands. That's why I'd recommend going to a shop and trying on helmets.

My Bells have usually run about $30 ... so you can get a decent helmet for a reasonable price.