Marksman or Bowmaster

Blizzard is nice, Puppet is nicer.

Blizzard and Arrow Eruption can't generally hit the same mob, it's honestly pretty annoying. Freeze one set of monsters, then bam Eruption hits 3 more that aren't frozen. You can use both, you just have to stick to 2-3 targets. Getting 6 in that right area is hard.

Depends on what you're referring to. These are not "one or the other" type of skills and are both useful in different scenarios. In a scenario where your Bliz & Erupt hits 2 different things, you puppet and you're happy. I use Ice way more at gobies, typhons (for lure) & newties than I do puppet. I'm too weak to judge skelegons so far.

In regular training scenarios, I very rarely use puppet since I got 3sec freeze. Ice is just quicker and actually does some damage too. That being said, I'm still maxing puppet because it's useful. Different skills for different situations. Because I don't really boss much yet, I would pick ice over puppet in a heartbeat, particularly since ice & frostprey lets you leave your eagle at 15 in third.