Barrayar would do well in martial arts, shooting, fencing and equestrian sports. Their track and field events wouldn't be particularly outstanding, nor the water events (and hm, this is making me wonder how the Nexus Games deal with genetic modifications of various sorts. Very strict rules about what is allowed and what isn't, I guess. I doubt Taura would be allowed to compete anywhere, nor Guppy, but I wonder about someone who's been specifically modified to be a brilliant sprinter or whatever. Tricky.). Team games would probably vary; Barrayarans are reasonably good at team play, but the non-martial sports probably don't get the kind of investment and attention that the martial ones do.
Specific characters: Aral is a boxer or possibly a judoka or wrestler (definitely NOT a sailor). (Actually, I saw a marvellous visual/mental model of Aral when I randomly watched a bit of judo - the Uzbek competitor Choriev. He just fit, somehow, in my head, he had the right eyes, and the right aura of being dangerous and controlled. And he was kind of ugly in the right way. You can see him prior to the Olympics, the guy in white here.)
Miles had to argue with a lot of people to be on the Olympic rather than Paralympic team, but rides in the three-day-eventing, following in his famous grandfather's footsteps, or should that be hoofprints (though Piotr's speciality was dressage, but there's not enough adrenalin in that for Miles).
Cordelia - for some reason I see her in an endurance sport, maybe in the Betan cycling road race team. I think the Betans do a lot of cycling, and gymnastics and sprinting and other sports that don't require open air or lots of space. Definitely no Betan sailing or rowing or equestrian team.
Ivan didn't make the cut for the football team and is secretly pleased about this because athletes don't get a lot of time for partying.
Alys and Illyan do ice dancing together these days (and I bet Barrayar is good at a lot of winter sports too), though Illyan previously used to beat all comers at judo.
Gregor - fencing, Barrayar's traditional sport, and he's very good. He loves watching all the really non-martial sports like rhythmic gymastics and diving and stuff like that, though.
And Mark is a wrestler and is appalled when people are reminded of his father's fighting style. More thoughts?
Crossposted at http://philomytha.dreamwidth.org/86