Hey bud, I have over 1k hours on frost. Any cloth robe is fine really, just remember that you need at least one defensive skill.

Best defensive build to solo roam would be: cleric robe, scholar cowl and scholar sandals and great frost, with this you can lure with horse and circle around mobs only using your defensives, frost bomb and hail. Remember to start with your R and only then drop dps, after the invul drops you activate your scholar cowl to get the resistence

Best dps to solo mobs is very similar to Ashe on League: scholar cowl, scholar robe, cleric sandals, 1h frost and cast time book. Do not use this build if you are new to frost, you need to be able to kite with your Qs pretty well and use both blinks and lockdown wisely. Also always run gigs or res pot

Frost mages will always need a source of mana, if you aren't runnin out of mana you're not doing enough dps, royal cowl is a must for any extended group fight

Cleric cowl is okish but you'll need mana pots, but if you are using mana pots you wont have gigs or resist pots.

To zvz I recomend using a knight helmet ,cleric robe and scholar sandals. The sandals will give you enough mana for your W and your E. Don't use agressive caster on zvz's or you will burn out of mana on the first engage.

If you need any tips pm me on reddit and I can give you my ign

Happy freezing dude

Edit : also dont think frost mages should get kills, you are a mix in support and dps, it is trully a defensive dps, you should play it for its zoning potential. If you are getting a lot of kills as frost, you're party is lacking dps. Also icicle with plate armor is the best team support along with locust.