play a fire mage, lock, hunter (BM especially), DK, warrior if you took msr and have spell reflect macro.
Or just have a healer who knows how to dispell, frost has very predictable burst and but not a lot of sustained dmg so keep pressure on them and make them blink first if you're melee
Very easy as a shadow priest. Actually I'd say you are being outplayed if you lose as a shadow priest against any other class than warriors.
Warriors on the other hand are kings of 1v1. To beat a (geared) warrior as a shadow priest I need to get him to 35% hp, burn his trinket and berserker rage (his two fear breakers, one with a 2min cd the other with a 30 sec cd), and then get him in a fear (he has to be cc'ed otherwise it's impossible to kill). Then I'll put up my dots, and then mind blast -> instant 3 orb devouring plague -> 2 shadow word: deaths. Hopefully I'll be able to finish these 4 spells before he is back on me (which is all dependant on where he ends up during the fear). Otherwise I'll have to rely on my 9% crit chance which isnt really that fun.