I don't generally mulch mine, at least here where I am - and that includes during winter too. I have a new little tree peony this year to go along with an herbaceous one that is going on its 3rd year here. I've found the soil mix that I used (Promix) doesn't dry out too quickly.

The main thing is that the top roots ('eyes') of the peony cannot be deeper than 5 cm under the soil. So if you plant it more shallowly in your container, you can add some mulch. If planted deeper, Peonies won't flower (for some reason that I don't know). Make sure you protect it over the winter though. Tree peonies are only hardy to zone 4, and I think Ottawa is zone 5.

I should've also asked whether it matters what kind of mulch I use? Is cedar mulch okay?

I have room in our garage to bring it in over the winter. Thanks for the tip!

Since you plan on bringing it inside out of the weather, it probably doesn't matter what kind of mulch. You may not even need mulch at all in a garage.

I love cedar mulch! Smells great, looks great, and can be mixed into the soil as it decomposes. Also helps retain water in the container, which is good for really hot and windy days and if you go on vacation. All mulch does that though, so you could pick something else if you wanted to.