Could I please put some thoughts in to your mind if you are thinking in this direction. Nothing drastic but maybe some thoughts you might not think about and will help you pick the right charity to go to if nothing else.
You are going to do some research and looking online, so their websites, pictures, staff pages on facebook, etc., are going to tell you a lot about them. Just read between the lines a little bit and really look at the pictures you see. Not just the pretty horse in the front, what about the background, fences, mud, general environment, etc. Don't forget about the Charities Commission website and look at the charity's finances etc, it is all there in the public domain.
Do the staff follow the values of the organisation (normally a charity), if they want a companion do they loan one from the charity or buy one in. Do they continue to breed their own horses despite knowing and dealing with the result of indiscriminate breeding? Or buying from auctions and then having to put their own on loan as they haven't got the room? Lots of things to consider here as the staff reflect the charity and they are the ones dealing with the animals on a day to day basis.
Is basic health and safety used within the charity. Do they wear riding hats (with the chin strap secured) whenever they are around the animals? Do they wear protective footwear and other PPE around the animals. No good saying they are good as gold, but they are animals and can still hurt you.
What are the animals being fed, how are they being fed. Simple things like feeding hay on sand, a big no no but it is done. I wouldn't like their vet fees for colic! Are the containers clean, the stalls clean, water containers full and clean. Do they accept medication from others, not a good idea at the best of times for humans never mind animals they are not prescribed for. Lots of little things that can add up.
As I say, it is the little things that can tell you a lot about the charity. Make sure you check things out, if you are not sure of the charity do not go there, go to one you trust after you have done your research. There are far too many equines out there needing forever homes, make sure you are going to take an animal on from a charity that is going to fill that space with a proper deserving animal rather than one from a sale or pound, etc.
Just a few pointers that might help you along the way, there is a host of information out there that is available to everybody, please use it to your advantage and I hope that you can find your lifelong companion through this means.
Can I please just finish on a point re laminitis. We will hopefully soon be enjoying better weather, so make sure you are observant and can restrict grazing where necessary. Plan where you can graze them now instead of having to suddenly find or make up a management or starvation paddock.
I hope the weather stays good for you all and we have some good hoof weather so that we can all enjoy our equine friends to their full potential! Most of all stay safe and if out and about do not forget your high viz whatever the weather and visibility! It can save both your lives!