running 2x4" vertically sounds a bit overkill to me. Structurally you'll only be supporting a couple of places where the bottom of the chest freezer has "feet" or bump outs. the 2x6s I used cover 80% of those feet and give me a large area to mount the caster. if there was anything I would beef up it's the casters themselves. Something with ball-bearing would make it loads easier to move around instead of the vulcanized rubber wheel on an axle. Even if the keezer weighed 1000lbs, each caster would only be supporting 250lbs which is well within the limits of a 2x4 or 2x6. I would also suggest using plenty wide wheels so you don't dent anything like hardwood floors or linoleum.
Hope this helps!