Tricky this time of year as everything is so dry. If the horses had stayed on further into the year, they would probably have flattened it out fairly well as it dried.
When it's soft, you can roll it, but beware compacting it as it'll prevent drainage which is probably poor if that size area has got so badly poached in the first place. A bit drier and you can run a spike harrow over it to kock off the peaks into the hoofprints and then roll if you want it very flat. You may have to reseed some areas. Failing that, plough, but it's somewhat drastic and will take years to re-establish as good meadow. Putting stock on, such as sheep will slowly flatten it out once it softens but I think you may need to look at the drainage as it sounds as though it must get very wet in winter if it is that bad all over!