Ticks have always been around Ottawa, and even in 2011? I recall -40C for well over a week, and obviously cold temps around that week.
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.
The lowest recorded temperature in Ottawa in the last 40 years was -33.1c in 1996. It hasn't been down to -40 since like 1911.
You might be recalling wind chill temperatures, which would not be relevant here. They're subjective perceived temperatures for hairless apes.
However it does occasionally get to (real) -40C ish in Edmonton area, and they now have populations of blacklegged ticks. But very small populations.
Like I said above, the issue is not the absolute lows or highs, it's durations of cold, which impact their ability to recover and produce large quantities of eggs in the spring. This was literally in an article I was reading about ticks the other day, don't make me hunt for it.
Black legged ticks are not new to Ontario, but they absolutely are to places like central Alberta. And the Lone Star tick is moving north for similar reasons and will be established here in Ontario shortly as well.
If there was more diversity in predators and prey, the population cycles would have smaller amplitudes. The large swings are often symptoms of a collapsing ecosystem.