Sorry you had a rotten day. Sometimes we have visions in our heads of how fun an activity will be, either because it was fun for us as kids or because it's something we always yearned for. Our psyches move ahead to the fantasy picture and not to the details of getting everyone properly outfitted. We forget that ice skating is difficult, kids don't have the ankle strength to keep upright, they don't have the coordination to move forward on skates, and all the other practical mattes such as the difficulty in fitting skates to feet.
We also forget that getting bundled up in winter gear makes going potty a huge hassle. The same thing happens when we sign our kids up for baseball - we envision a beautiful day, lots of good sportsmanship, and everyone having a good time. We don't envision that kids can't hit, don't know the rules, or spend time in the outfield wishing for juice and potato chips while hoping to God no one hits the ball to them.
Try to remember that hikes in the woods incur mosquitos and poison ivy, beach days involve sand and sunscreen, and hauling a lot of gear from the parking lot, plus some noisy teens on the next blanket. Big birthday parties can involve kids getting "the gimmies" when all they want to do is open gift after gift without saying thank you, while all the other kids are bored to distraction watching their friend open 25 gifts!
What I do is try to scale back - for example, I might try roller skating instead of ice skating - still hard, but at least it's not so cold and it's easier to stand up. I'd also try some other fun activities that don't require as much equipment or preparation. For example, getting a free pass at the public library that gets me and my kids into a local museum feels like fun- and if they get cranky and want to go home, I know I didn't pay full admission fees.
Try to have an extra adult on hand, and not to take on more than kids are old enough and coordinated enough to manage. Have birthday parties with 6 kids, not 25. Take on activities appropriate to your kids' developmental stages - try some scooters or rip sticks instead of ice skates, try a small indoor play area that doesn't require a lot of skill, or a small hands-on kids museum.
As for dealing with defeat - remember that the best baseball player in the world only gets a hit 1/3 of the time, the top football quarterback has lots of incomplete passes, and the top author went through 12 drafts before getting a publishable novel! Also try to find joy in the little stuff rather than the expensive involved stuff that needs a lot of prep time. You're not a failure - you're a parent who wanted her kids to have a great experience. It didn't work out. That's not failure - that's life. It is a learning experience. And you'll teach your kids to bounce back better from disappointments and defeats if you don't label everything as a contest to be won (even if you're only competing against yourself). You're not defeated - you just overestimated.