What are the snowshoes criteria that I should look for if I want to snowshoe on a hilly terrain ?
Elevation bars are great, but more important are the grips/spikes on the bottom, not just for icy snow, but for fallen wood/exposed roots which are especially slippery in the winter. That traction makes all the difference. Ideally the grips run parallel to the length of the snowshoe, usually to the outside, and an additional grip runs across the toe where it descends through the shoe.
One additional note on elevation bars: you'll want a boot with a sole that's rigid (like a hiking/climbing boot) and not a softer soled boot like a mukluk, as there is no support between the hell resting on the elevation bar and the ball of your foot. You'll also ideally want to find an elevation bar that can be raised/lowered using a hiking/ski pole so that you don't have to kneel down to activate/disable them.
Poles will help with stability, and make it a lot easier to get up when you have a pack and you've fallen in deep snow.
I would consider two items:
And if you are looking for a pair of modern snowshoes
It is common to use the trekking pole to flip the bar up when required.