The typical "tweaker" sorc (focus on Fast Casting, +Cold Damage, -Enemy CR, Frozen Orb and Cold Mastery) will get you all the way to Act V Nightmare pretty much by yourself if you take your time. Frozen Orb is the uber-Cold spell, basically a sphere of pure cold that throws out Ice Bolts in all directions. It's virtually impossible to miss with it, and when you pump it it starts doing some serious damage.
EDIT: Unfortunately, they nerfed FO slightly with a one-second cooldown since I last played, and other spells have gotten better with the synergies; currently the most powerful Cold combination for a true "tweaker" build is Blizzard + Glacial Spike. Max those two, plus Ice Bolt, and you'll deal triple damage with Blizzard, while doubling GS's damage and giving you 60% longer freeze time. FO is now best used by a "fire and ice" build like the Meteorb, as a wide-area yet mobile "freeze-frame" to hold your enemies in place for the pain raining down from a Meteor, Hydra, or your allies.
Once you get to Mt. Arreat in the Nightmare difficulty, a lot of the big baddies you'll meet are cold resistant/immune. You can overcome this with decent Cold Mastery (unlike Fire Mastery and Lightning Mastery which increase damage dealt, CM decreases enemy Cold Resistance which strips immunities while having the same overall effect of increasing damage taken) but sometimes you have to max it, plus find additional help in equipment and hirelings (the Conviction paladin aura stacks with CM, as does the Necro's Lower Resist curse). As a few enemies have 251% Cold Resistance (and so even with CR reduction capped at 150% they're STILL immune), it generally helps to have a couple other tricks up your sleeve.
If you go for Fire skills, watch out; in Hell difficulty, EVERYTHING is Fire resistant or immune. You will find your combat effectiveness shrinks to almost nothing without some serious help from resistance-stripping allies. Despite this, I found Hydra to be a very powerful friend for my Sorceress build all the way through Nightmare difficulty (my only failing was focusing on the Fire tree not knowing Hell difficulty would nerf it). Meteor is a good substitute especially for large crowds, and you get it earlier meaning you can put more points in it through Normal difficulty (You should try to gain 10-15 levels for each Normal act if you are soloing, meaning you'll already be in Act IV before you can put the first point in Hydra). And you should always put a few points in Warmth for free equipment-independent mana regen.
Two other spells you simply must put points into are Teleport and Static Field, from the Lightning tree. Both of these skills are very powerful from the very first point invested; Static Field drains 25% of any nearby monster's HP in one hit, and it has virtually no cooldown so you can cast it four or five times in succession, then follow up with another spell like a Frozen Orb or Meteor for the coup de grace. In Nightmare and Hell difficulties, Teleport will get you out of a jam, and if you decide to play with a group at any time, Mephisto runners will expect you to have the Teleport skill so you can get them to Mephisto without crawling through the single largest dungeon in the game (in Hell difficulty). Neither of these benefits much from maxing it (Teleport's energy cost goes down by one with each point, while Static Field's range increases by .6-.7 feet), so you can save your points for offense.