I have thought about a horse generator, but also making the horse size, carrying capacity, will, etc. similar to that of true terrn breeds the horses are modeled after. Here are some rough ideas for types -
1) The Draft - Modelled after the "Fjord Horse, thought to be the most similar to early draft type horses (and of of the orginal 4 types of Horses)
Height - 13-14 hands, weight 880-1100, cold blooded
2) The Arab - 14-15 hands, 800-1000 pounds, hot blooded
3) Akhal Teke - 14-16 hands, 900-1100 pounds Hot Blooded
4) European Warhorse - Modelled after a handful of type, most notably the Lippizzaner, Frisian and Andulusian - These can be made more sepcific if need be 14-16 hands, 1000-1200 pounds. Warm Blooded
5) The "Celt" - This is more of a horse I came up with, perhaps similar to the warhorses used by the Celts in Europe, with some breeding with native european stock, and not a huge organized focus on selective breeding.
13-14 hands, 850-1050 pounds, warm blooded. Would also be considered the Rouncy of Middle Ages fame.
6) The Chelni/Hodiri Pony - Modelled after the Fell pony, this is a great fit. Usede by the Romans in war, also bred with other horse in Britain to produce a British warhorse from native stock. Has many aspects of a hot blood, including nimbleness, speed, and carrying capacity for weight. It's temprment was more like a warm blood though.
12.5-14 hands, 900-1050 pounds
A few notes:
Hot Blooded would have higher agility, speed, and will
Cold blooded would be lower in speed and will, average in agility
Warm blooded would be a combination
Ponies - Good agility, speed, average will.
Maybe 3D6 for will, Cold blooded re-roll any 6's, Hot bloods re-roll any 1's?
Agility - Hot Bloods and Ponies re-roll any 1's
Carrying capacity before encumberance begins:
Hot Bloods and Ponies - 27.5%
Warm Bloods - 25%
Cold Bloods - 22.5%
The star rating of the breeder would effect stats to an extent, and would effect beginning initiative even more.
Just some preliminary ideas here