We haven't bought a lot of minis (6 to be exact) but we did a lot of thinking about this very issue along the way. We bought 3 of ours as babies and the other three as 2 year olds or older. The older ones were all purchased in January in the Northeast, so we still didn't get a good look at what we were getting. But we did a lot of homework in all cases. Also, personality, movement, and nice heads are important to us, and those can be evaluated as babies or in the winter.
It seemed to us that the best selection came with babies, and this seemed especially true if you were looking for a really top notch prospect. We bought the filly in my avatar sight unseen based on photos, a tape, our impression from meeting a half-sibling, the reputation of the breeder, and close inspection of the Stud Book online. We checked sibling show records, the production record of her dam (13 babies, including World Top Tens)... you get the picture. Of course we were gambling on how she would turn out and still don't know if she will be able to produce. We also bought another filly and a colt as babies, that we did the same homework on but were able to see in the flesh.
The ones we got in the winter included a gelding that was a 2 year stallion that the breeder gelded for us. He doesn't really count because he was our first mini and was purchased to be a companion for our big horse, but he has been a successful show horse too. We found that winter is a good time to find relative bargains on "older" minis as people make room for new foals, etc. We get photos and tapes for any prospects and have rejected a couple of horses based on their moverment shown on tapes. Ironically our last purchase was a proven broodmare that originally came from Cathy-H! She has the sweetest personality, lovely movement, and has already produced 2 fillies, one a grand champion. She arrived in an ice storm last January. We admit we did get a bit tired of waiting for the young fillies to grow up before we can breed them and we wanted a proven broodmare to start with. Plus we want to continue the show the black and white filly this year. We will be trying to breed the other mare that we got in the winter who is coming 4 now. We did note from her registration photos that if we had seen her as a baby we would probably NOT have purchased her. Nothing special about her registration photos, but she matured into a very nice little mare. So you never know....
Good luck with your shopping.