>>2794481You need it for deep snow - powdery uncompacted snow, fresh snow on a high mountain. If you've ever been in snow like that, you would know it, and realise "damn I wish I had snow shoes". It becomes impassable.
If that hasn't happened, then no, you don't need snow shoes. The boundary is when it's far above your knees.
If the snow is firm, wet, not deep, or been compacted and/or had many other people walking on it (e.g. on a trail), then you don't need snow shoes.
Once the snow is up to your thighs it's just really impossible to make any progress. It's not walking any more, it's digging yourself out of a hole only to be in another one. You can't lift your knee up any more because of the weight of the snow, and if you go higher into the deeper snow, you risk falling up to your chest or more. The only option unless you want to die is to go back the way you came. And remember next time to bring snow shoes.
If you are just walking around in some snow of a few inches or feet, then sure, boots are fine. If the snow is deeper than your boots, use gaiters to avoid getting snow in your boots and getting wet frozen feet or frostbitten.