As far as cold feet, I think it is a common problem, especially with clips. You have a few options but some experimentation might be necessary. As mentioned by
@Paul H you can add toe warmers to any of the following solutions as well.
Option 1:
2 pairs of socks and a "vapor barrier." More specifically, wear one pair of socks, put a plastic grocery bag over each sock, put on a second pair of socks over the grocery bags. This will prevent the cold wind from getting to your feet and any foot sweat from being exposed to cold air. Quality wool socks will make this solution even better. It's a bit ghetto but I have done it many times and it works.
Option 2:
Obtain a set of windproof shoe covers that will go over your riding shoes. These can be had cheap on Amazon, as a quick fix, or you can get name brand options for a little bit more. I have some cheap ones and they work fine, for now, and still allow the cleats to interface with the pedals just fine.
Option 3:
Put flat pedals back on your bike and wear proper winter boots (not riding specific). You might be giving up some pedal grip going this route but you'll be warm.
Option 4:
Buy a set of clipless winter riding shoes. This will be your most expensive option, by far, but is probably the most elegant way to stay warm on a bike in the winter. I have not ponied up for a pair of proper winter riding shoes so I cannot make any recommendations.
As far as cold hands I would suggest getting some windproof, insulated gloves. Again, they can be had cheap on Amazon or you can spend more for name brand stuff. Alternatively you could get Pogies but I personally don't think they are necessary in our area. I have ridden in single digit temps without them and have been just fine with good quality gloves.
One other point to note. You're extremities will feel colder if your core is struggling to stay warm. This is a tricky one because overdressing is not great, either. The sweat you will generate while being overdressed is a major problem if you have a mechanical or need to stop for an extended period of time. If you don't have a hat for under your helmet I would suggest getting one as a lot of heat is lost through the head.
It will take some trial and error to sort all this out. Everyone handles the cold differently.