There are really only two things that happen at the winter meetings that are of any interest to fans. One is a lot of talk that might lead to free agent signings or trades. The other is the rule 5 draft. The Twins will likely be involved in both.
On the free agent front, the Twins continue to talk to their remaining free agents, Capps, Cuddyer and Kubel. Of course, other teams are probably talking to them too. Its possible the Twins would make a trade or sign a different closer than Capps, but I think its likely any other outfield deals will wait until Cuddyer and Kubel are out of the picture. I have to admit I am sort of hoping Cuddyer goes elsewhere. They need a right handed bat, but signing an aging outfielder to a multiyear contract is a step in the wrong direction. Kubel is younger and may be available for a shorter contract, as well as less money. The most likely free agent signings are bullpen arms.
On the trade front, a starting pitcher would be the likely target. In terms of players leaving. I think Kevin Slowey would be the most likely player dealt. Jose Mijares would also be on a short list of potential trade targets, given he is arbitration eligible. Francisco Liriano would probably be available for the right price, but I doubt anyone will pay that price.
I expect the Twins to take someone in the rule 5 draft. People talk about start taken like Santana et al, but its important to remember draft eligibility has changed since the Twins took Santana. With an extra year of development the chances of finding a diamond in the rough are even slimmer than they used to be. Given the Twins bullpen situation, I would expect they add a more experienced pitcher they think can help this year, rather than someone with huge upside.
You may remember the Twins traded Jarret Camp for Santana and cash after taking him just ahead of Santana. Camp was seen as the player in the draft who was most likely to provide immediate help. Florida, drafting after the Twins, wanted him. So they paid a bit of cash to make sure they got him, while the Twins got the guy they wanted This year the Twins are more likely to be the team getting Camp.
In any case, I would not be surprised if nothing much happens this week on the Twins end. Lots of talk, but no decisions is par for the course.