I used wet bags too---great because you just throw them in the wash so (at least for me) it's less work than washing Ziploc bags and cheaper than buying Ziploc bags if you're using one a day. I like PlanetWise a lot. During the day between sessions, I store the horns in the cooler I use for milk, which goes into the office fridge.
Quite honestly, though, I've gotten pretty lazy in my last weeks of pumping and now often just toss the horns in my pump bag at the end of the day. Probably not wise over long periods of time, but I wash the bag periodically and it hasn't really been an issue.
I second having two sets of pumps, although mine are in rotation since I don't pump at home. So the ones I used today will go into the dishwasher when I get home tonight, and I'll pack up the other set to go to work tomorrow. Since we run the dishwasher almost every day, this works well.