Tampere is located in Pirkanmaa and in Häme.
Most of the riding stables located in Pirkanmaa or in Häme can be found on these two websites:
1) hevostalli.net - Tallit=> Pirkanmaa
2) SRL - Tallihakuri=> http://www.ratsastus.fi/ratsastuskoulut_ja_tallit/tallihakuri
=> Choose "Häme" and then "Hae" (Search) OR just write the name of the town/municipality under "Etsi kunnan nimellä" (so write Tampere or any of the municipalities near Tampere)
Most of these riding stables don't have any text in English on their website, but you can always try calling. Every riding school website should have a phone number visible.
For example, these two riding schools are famous in Tampere area and also easily reachable by bus:
http://www.niihamariding.fi/ (located in Niihama, Tampere)
http://www.equillence.fi/in-english/ (located in Kangasala)
They have professional riding teachers who also speak English.
More information:This official horse riding website has some information in English:
=> "In English"
SRL = Suomen Ratsastajainliitto = The Equestrian Federation of Finland