This is an episode that was pretty good despite itself. You pointed out most of the plot holes in it, but it did have a feel that they really were pioneers in space exploration. The broadcast to the school children was a nice touch, though even that was lazy writing since they addressed this to... one classroom instead of a broadcast directed at all school kids. Also, can you email and print crayon pictures in the 22nd century? Advanced technology there.
My favorite part of the episode had to be the snowman. Sure it was silly, but that's the point and at least they weren't ONLY dicking around on the planet like in Strange New World and actually working on what they were supposed to be most of the time. Though I like how the snowman grew pointed ears when Archer told them the Vulcans were watching.
Trip and T'pol's interaction really seemed like a missed opportunity to me. Not with them, they're doing their best to slam Trip and T'pol together with all the subtlety of a bull in a china shop, but with Hoshi. She decodes the message... then just conveniently doesn't look at it, so Trip can do the big reveal. It would've been nice to give her SOMETHING to do and sharing a personal secret with T'pol would've been nice.
If more season 1 and 2 episodes could've captured this atmosphere I think the show would've been better received.. at least by me.