Do winter snow running boots exist?

After a year of use the bottoms of the boots pictured have became detached and snow and ice chunks get trapped between the rubber and the upper.
The boots have worked good enough until they broke. Ideally they could be a little higher / taller for going through deeper snow.
I go running with dogs "canicross" sometimes we have to blaze a trail through snow sometimes there's icy areas.
I've been searching but have not found an ideal boot for this use yet.

Does something exist that has good snow / water protection, traction, lighter weight, a design that doesn't break like the boots pictured.

Basically a snow running boot.