Some tips to non-weather teams:
¤ Make sure your team can take out weather users AND non-weather users. Not everyone uses weather!
¤ Try replacing a move on your team with sunny day, sandstorm, hail, or rain dance (depending on which benefits team most) so you can turn the tide of a battle against a weather user in your favor. For instance, on my Jolteon I replaced shadow ball with sunny day for use after taking out the weather starter.
@Op, yes non-weather teams are viable! They give a lot more opportunity to be creative- to build an effective one, skill/experience is needed!