Yeah sure, if shrubs or small trees are being strained by weight, knock off snow if you can.
If the weight is mostly ice & it won't come off readily with a simple blow of a snow shovel or whatever, then you probably ought not mess with it at all.
Certain species of grass are more susceptible to snow mold than other species.
Around here, we see it more in bluegrass & ryegrass lawns.
Almost never in t.t.t fescue lawns.
Here's a very good fact sheet about snow mold from U. of Rhode Island & UMASS:
A wintertime pet peeve I & many other older folks in this biz have shared for years is the increasing practice of walking / driving over turf that's frozen or heavily frosted.
Anyone who's been around long enough will know not to 'crunch around' on unprotected frozen grass.
The weight of equipment &/or bodies on frozen turf at the wrong time become evident sometimes weeks or even months later in the form of damaged plant cell walls, often all the way down to the turfs' crown.
Ugly cosmetic damage from this will appear to your client as the turf begins to come out of dormancy in the form of streaky wheel tracks & phantom foot prints. They may wonder just what caused it & call you to ask!
So obviously the solutions are, depending upon the job task-at hand, to wait until the turf defrosts before you go about your work, or to wait until the lawn is covered with a reasonable blanket of snow.