Books: Thrush is a potential issue with all the wet weather, and the first sign is that the frog smells, but is also soft. You'll know if you smell it! If you catch it early it's easy to deal with (hibiscrub and purple spray) but if left it causes lameness and can become chronic. The main thing is just to know how your horse looks, feels, smells and acts when well then anything different means that you know when you've possibly got a problem.
For tack checking you need a qualified saddle fitter. You should always have the saddle fitted when you get a horse as it needs to fit horse and rider and may need to be adjusted if you are a different size/weight from the previous rider. You should have it checked anually, or sooner if the horse changes shape significantly (ie gets fit, loses weight etc)
We have the ponies backs done by an equine physio twice a year (at the beginning and end of the show season) The horses who just hack mainly get done once a year. Some people swear by Mctimmoney for backs. Check out who's registered in your area and google/ask around for reviews.
Don't wory too much about your cob's feathers. Mine has loads, lives out all year round and has never had any problems (other than them looking a mess when it's very muddy) but I do keep a careful eye for her stamping etc as that can indicate mites or irritation from other issues and I wash them regularly in hibiscrub to keep them clean.
I also should have put a good hoof dressing on the list. We do all of ours with Kevin Bacon hoof dressing at least once a week, more often if it's very wet or very dry. Do the sole as well as the hoof wall.
When we moved off full livery worming was one of the areas where I felt I needed to learn more so I signed up with Intelligent Worming who do a risk assessment questionaire, poo samples for egg counts and devise a programme which comes through the post as needed. I've learnt loads and I know that the horses are properly protected.
Sorry, going on a bit, got a piece of work I'm putting off so procrastinating in here. Do you have geldings? If so we need to talk about sheath cleaning 