This isn't something I've done myself but the obvious database approach would be to look at the in_race_comment field from the historic_runners table.
This tends to include several comments on a horse's performance, separated by commas. The segment before the first comma would give a fair guide to a horse's basic running style ("held up", "chased leaders", "led", etc.) especially if you look at multiple performances for a horse.
It'd take some work but it would be possible to write a script to parse and analyse these comments automatically as part of a daily update routine.
Alternatively, the Betwise site includes a live list of "leaders and laggers" for the day's races, updated here: http://www.betwise.co.uk/leaders_and_laggers.txt