Could I have damaged the bearings/cone when replacing a tire? Front wheel wobbles side to side Last evening I installed new tires on my bicycle. The front wheel now wobbles side to side. I notice a small movement about 1-2 mm near the hub/axle cone.

I checked to see if the skewer is all the way set in the fork brackets, also checked that skewer is tightened firmly. The wheel is properly aligned in the center.

After reading this post (How do I know if my cone/cap/bearings need to be adjusted?), I reckon that my wheel's bearings may need to be adjusted/replaced; I recently had my wheels trued at an LBS. 

There was no wobble before I changed the tire. Is it possible that I could have damaged the bearings/cones while putting the wheel back? 

Inputs on how to avoid this next time are welcome; as I will be changing to wider tires during the winter commute.
Any time you change your tire it's a good opportunity to check the condition of your cones and bearings. 

What sometimes happens is that the cones or retention nuts are starting to loosen, but the compression of the mounting nuts or quick release skewer holds everything together tight enough that you don't notice. After changing the tire, you may install it with less tension on the mounting nuts or skewer, and this allows the slack in the system to be noticeable.

It's easy to fix with a set of cone wrenches, or a regular combination wrench. An advantage to specialized cone wrenches is that they are normally thin enough to tighten or loosen the cones while the wheel is still on the bike.

It's unlikely you damaged the cones or bearings while changing the tire, but you can destroy the entire hub very quickly if you ride on a hub with loose cones.