The only real way i can think of is with animal lore, i could be wrong.. but i have never seen any gains in the journal or on the screen when any pets gain in stats/skills.... the way i did it was get my tamer to train him and keep an eye on his skills then trade to my warrior

The only way to tell the gains for animals is by using animal lore. What shard are you playing on? Maybe you can hook up with someone from this forum to lore your horse to see how it's doing.
Archaon...I have trained up my blue beetle some, unfortunetly he thinks he can kill anything now and takes off on a whim. My fire beetle is still a wimp. He takes fooooooorever to kill a rat or mongbat.

LOL its funny you should say that my blacksmiths fire beetle took forever to kill a cow i couldn't believe my eyes when it took so long to kill this cow that my blacksmith with little combat value had to join in and kill it....

and I know what you mean with your beetle my swampy now seems to thing its the big dragon on campus and struts around taking things on when it shouldn't... good job its bonded, its had its head weived into the ground a few times

I trained up a chicken once to 3xgm, 125 on the stats. He was one mean mofo chicken! I called him Tyson. I trained him in the Jhelom bullpen, and by the end was able to wipe out the bulls in a matter of seconds. I never brought him out to do other stuff tho, as the event we were gonna throw ended up not happening, and I just released him into the wild.. Although it was alot of fun fighting with my guildie's chickies..

oh my god 3xgm kung fu Chicken, that must have taken awhile!! awesome

Yah it wasnt a quick process, but this was when I was at a very bored time in UO. It was before I started pvping, and already finished out my 120 across the board tamer, and wanted to throw a chicken fight night event. I would say it took about a week or so. I was helping a friend who was building up his taming, so he was out there healing the chicken, and raising his lore/vet skills. So it helped out both parties