If your horsebox is non-compliant, so Euro V emission standards or older, then it will be charged in the Clean Air Zone.
If it is classed as an LGV then it would have a temporary exemption to 31 May 2023. From 1 June 2023, there will be a daily charge of £10.
If the horsebox is classified as a Private HGV, then there is be a permanent discount in place, which you would have to apply for. This discount would mean that the daily charge would be £10, rather than £60 per day.