Overshoes are pretty good on the MTB as far as keeping the feet warm and dry. Problem is they tend to be fragile if you’re stepping on rocks etc in the course of a ride – I’ve had several pairs and they’ve all torn eventually round the base (some in just a couple or rides).
They’re cheaper so I’d certainly give them a go. Long term though you’re probably looking at a false economy. How long does a shimano winter boot last – 3 yrs or so IME, costs £100. How many overshoes would you go through in that time – way more than £100 worth I reckon. Plus the normal wear and tear on whatever shoes you’re wearing underneath them.
Just my experience – maybe someone can recommend an awesomely durable overshoe.
Minor point is that they’re a bit of a faff compared to just sticking a normal shoe on and hitting the trail.