It impacts the population, but even a couple solid weeks of -20C weather doesn't seem to be enough to eradicate them.
Insects lay eggs, and also go dormant under fallen leaves typically. The snow + leaves insulates them, it's how live insects survive the winter.
If you watch robins in the spring, before the ground thaws, you'll see them flipping over leaves. They're eating loads of insects hiding, most still torpid from the cold.
-40C isn't a problem for ticks to live through in this way.
In terms of population, everything follows predator/prey cycles. Nothing is static. It's normal for populations to "explode", eventually predators will grow in numbers too.
I see it with noseeums here, and dragonflies. There are almost no noseeums this year, but loads of dragonflies, which means the dragonfly population will collapse, and soon (couple of years) the noseemums will be relentless. But then the dragonflies will grow in numbers, with plentiful food, and the cycle will repeat.
It's natural.
Global warming may shift habitats, but these ticks are normally here. They're not new.