Couple of points I've found fishing a relatively small stream this winter - possibly smaller the BA but I think the principles remain the same....
Trotting - really good idea for searching fish out, you get to cover way more water than you do with a feeder. So a great tactic for location. Personally, I really enjoy it as a method too, as you can travel really light - rod, net, maggots (I have a bait pouch with maggots plus spare shot, hooks and a disgorger round my waist). Fish a run for a few casts, if you get bites it's worth staying and putting a bit of effort in, but if nothing happens you just move on. To keep this simple, I would only use maggots - and keep my expectations pretty low. If I'm getting bites - from anything - that will do. Gradually over a few sessions, you'll build up a much better idea of the "hot spots" - and then you might want to try those areas with different methods (feeder etc.)
Depth - what I've been finding with the stream I'm fishing is that (unlike in the summer) if I can see the bottom then there won't be any fish. Whereas any of the deeper areas - say 3 foot plus - have a very much higher chance of holding fish. I think this is because water clarity is pretty high at the moment (cold weather + no rain = clear water) but this might be different where you are? Anywhere you find deeper water is worth investigating, and don't be afraid to tinker with the depth of the float. In some swims I'm literally changing it every cast, just to see what happens. Sometimes you'll find swims where the float will still go through, even though you can see the hook is hitting the bottom. This is usually a sign that the bottom is likely to be gravel - so if you've got deep water over a fairly clean gravel bed, that's an area worth spending a bit of time on.
For feeder fishing - liquidised bread in a small feeder with bread, worm or maggots on the hook should see you get bites. Again, don't be afraid to move around a bit. Whilst its certainly true that the fish aren't as well spread out as they would be in the summer, it's also the case that if you find them, there's plenty that will still feed (roach, chub, dace and perch are all realistic targets). I tend to cast out and count very slowly to 100. If I don't get a bite, i'll retrieve and cast in to the same spot and give it another go. Repeat one more time - if I haven't had a bite on that third cast, i'll start thinking about moving. Like you say, there's loads of nice looking spots, so best to keep trying. (Of course, if you get bites - fish it out!! See what happens - you might find a swim where you'll catch all day)
A few sessions fished mobile like this - with float or feeder - will give you a much better idea of where the fish may be. Then as you progress, you can start making better decisions about where to start the next time.
Good luck! As I said on another thread about fishing mojo, I love this time of year! Yes, they don't catch themselves - but the fish you do catch are a little harder earned and so also more rewarding. Tight lines, and let us know how you got on!