Never sure exactly how high they go at county level, it normally depends on the show.
The heights from BSPS rules for the open classes:
Heritage Cradle Stakes - Min 47cm, max 53cm, spread 47cm
Heritage Nursery Stakes - Min 47cm, max 66cm, spread 47cm
Ponies not exceeding 122cm - Min 53cm, max 74cm, spread 53cm
Ponies not exceeding 138cm - Min 69cm, max 84cm, spread 69cm
Ponies exceeding 138cm - Min 84cm, max 99cm, spread 84cm
The heights from Ponies UK rule book -
Beginner Stakes - min 40cm, max 55cm, spread 45cm
Nursery Stakes - min 47cm, max 60cm, spread 47cm
Not exceeding 122cm - min 58cm, max 74cm, spread 53cm
Exc 122cm but not exc 138cm - min 69cm, max 84cm, spread 69cm
Exceeding 138cm - min 84cm, max 99cm, spread 84cm
For shows that are affiliated to a society, the heights can be found in the rule books, which are available online.
It varies! Depends on the shows, and the entries I think. Uusually about 2ft, sometimes they have them small for the smaller breeds/kids and put them up for larger breeds/over10s. At the most I'd think 2ft3, but I think it's not so much the height as the scariness - have seen skinnies, ditches, shiny beer barrels, bale of straw etc. along with rustic poles, brush etc.
BSPS split by height as well as nursery/cradlestakes.
Under 12hh novice is up to 2foot, Under 13.2 novice is 2'3
Under 12hh restricted is up to 2'3, the 13.2's 2'6
Open 12hh is 2'6 with the 13.2's 2'9.
Cradlestakes is 1'9 and nursery stakes 2'3.