Mutations occur primarily during DNA replication, early in cell division. Not a lot of that going on in resting yeast cells stored at fridge temperature.
Freezing (and thawing) can, amongst other things, have a significant damaging effect on exposed mitochondrial genomes producing petit mutants. This can produce wide-scale mutation-like effects on behaviour of the nuclear genome, which mitochondrial genomes interact with at a high level. Why it’s considered good practice to QC brewer’s yeast on agar plates post thawing, to select healthy-looking colonies. The frequency of petit mutant colonies is strain specific (e.g, determined by the level of endogenous trehalose produced) and affected by procedure, biological integrity, cell tolerance, etc., but they can occur at pretty high frequencies. They grow in starters and fermentations, but not necessarily true to strain characteristics. It risks non-numerical under pitching, aberrant fermentations, funny of flavours, etc. I haven’t observed many genuine-looking petit mutants from samples stored in the fridge so far. It’s not so much mutation that’s the problem with storing yeast at pitching volumes or greater in the fridge, it’s the fact they lose vitality and die at a rate over time, soon becoming a risk for under pitching. Not really the case with small samples.
Consider brewer’s yeast remain viable in small samples in beer bottles kept cool in ship wrecks for >100 years.