Changing a clutch on a bike is EASY. You need to drain the oil and then remove the clutch cover on the side. Put the bike in gear and have someone press the rear brake while you unbolt the pressure plate bolts. Remove the pressure plate. Pull the clutch plates as a pack. Check the metal friction discs for wear while they're out. Slide the new discs onto the clutch basket and alternate between friction pad and metal disc until all are on there. Put the pressure plate back on. Put the springs on and tighten the bolts down to the proper torque. Install the clutch cover with a new gasket. Filler back up with oil and you're done.
However, the typical sign of a worn clutch would be SLIPPING when accelerating. The engine will rev up but the bike won't actually increase in speed... feels kinda like a slipping rear tire but no sliding feeling.
Not going into third sounds more like one of these: incorrectly adjusted shifter lever, shifting like a wussy and not pressing it into gear with enough force, not pulling the clutch lever in all the way (or an incorrectly adjusted clutch lever, or problems in the tranny itself.
My bets would be on a clutch not fully disengaging due to the clutch lever not being adjusted tight enough, or just being a general pansy when shifitng (no offense meant).
(You also said it happens when it's cold... that's proabably caused by the oil being cold/thick. The oil will actually cause the clutch to grip in this situation.. letting the oil warm up, using a lighter weight oil, or switching to synthetic should resolve that problem.)