Winter boots or neoprene covers?
For pure road-riding: Neoprene covers over normal road-shoes are the best as long as you don't have to put a foot down too often. The cleats are prone to clogging in snowy conditions. But then you wouldn't certainly get on a bike. On the other hand, ankle hugging covers keep the rain running down the legs into the shoe, which could happen with insulated boots.

For cross-country riding or commuting: Specific insulated and waterproof (membrane-type) shoes with profiled soles for MTB-cleats and MTB-pedals are a very reliable solution. MTB-cleats and pedals by design cope better with adverse conditions like mud and snow. And the shoes are more wear resistant than covers if you need to walk longer distances and there is less trouble to put them on and take them off.