I’ll give my 2 cents to the archer experience. My pvp experience with an archer is pretty good. I use a few different classes, but my night-blade does fairly well. I have him set up as a ganker, so most encounters end rather quickly. And I use mainly bow skills to inflict 90% of my damage. And to the encounters that don’t end fast, I usually have an escape already laid out. Especially if I have time to set up my shade around a corner or on a 2nd story ledge, I just teleport to my shades spot and reset the encounter or break off. 80% of my battles end in success cause I can look at the health of a target and gauge if I can take them out successfully or not. If the health is too high, I don’t engage or I follow them until they get distracted and attack.

If you are talking about straight up open engagement then I can’t help you. It can be done, a quick search on google or YouTube will give some insight into players who can go 1v1 or 1v(group) with relative success and the builds/skills they are using. I’ve seen one guy who is quite successful with a necromancer bow build and he wreaks shop in battleground or open field pvp.

As far as an ice mage play style. I’ve done it. Mostly for my nord, Warden, ice staff tank. I used only ice themed sets and my main bar was mostly ice skills, and it worked wonders. It is not quite as pure an ice mage but it got relatively close as far as ESO goes.

if i see someone with a bow or shooting green beams I know its free eats.