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.