As Loosie has said, get rid of the clover. This can cause multiple problems for most horses. There are many ways of doing this - some people spray it with a broad leaf spray - personally I hate the idea of spraying anything so what we do is run a mob of sheep through pasture with clover just before the horses graze it. Don't leave the sheep there too long. What I've found is that clover is the FIRST thing sheep go for, they LOVE it. The other thing we do is we never graze short grass - we make sure that every time our horses go into a new paddock, the grass has seeded and is long and rank and fibrous. Clover doesn't stand a lot of chance in the long grass. A little bit of clover here and there won't hurt.
Don't fertilise, this adds nitrogen to the soil (as does clover incidentally) which is the last thing you want. Horses need rough UNFERTILISED grass.
We do top with lime once every couple of years and occasionally use a natural soil conditioner which helps the microbes and worm life.
For me, with multiple horses, this means I lease paddocks in the district for about 7-8 months of a year - a pain, but so worth it as we only have 11 acres. Other people feed hay most of the year - that is another option.
Secondly, assess what is already in your paddock - what you want is native grasses and grasses like Brown top, Timothy, Cocksfoot, Prairie Grass, Yorkshire Fog etc - a good mix of many species in other words. (I don't know what grows where you are but what you do NOT want is clover or rye.
A lot of people think that horses should be on lush,short green grass when this is the LAST thing you want a horse to be on. You will be amazed how well your horses will do on the rough stuff - that's what they are designed to eat.
As an example, this is my yearling galloping around in his 'crap' grass paddock.
I think you get the idea, not a blade of green to be seen and don't think he looks like he suffering The only time he gets green grass is for a few short weeks over spring and possibly autumn.
We never fertilise OR irrigate. He gets a daily feed (beet, copra and oaten chaff) with 1 Tbsp SALT, a quality mineral and, because our soils are very boron deficient (which causes magnesium deficiencies) an added magnesium supplement.
Hope this helps