How hot or cold would it have to be before cybernetic implants began to become uncomfortable, or distracting to a PC?

As an example: If a character had titanium bone lacing, wired reflexes rating 2, and a set of cybernetic eyes and traveled to do some work in Athbaskan Council and found themselves in the mountains during the winter how cold would it have to be before he or she "felt" the ware? How cold would it have to be before it became uncomfortable?

The eyes would be a major concern. But not as much as you'd think. Biological eyes are a good part water (Well, liquid), and freeze badly and painfully (Personal experience. I got inside as quickly as possible when the hurting started) in extreme cold. Cybereyes won't have that issue, and the electronics inside might even keep them warmer than regular eyes might. Maybe. The metal might also transfer the cold to the socket, which might cause, well... Stick your tongue to a flagpole...

Bone Lacing and Wired Reflexes wouldn't matter, those are so internal that by the time they're hit by ambient temperature, you're already in serious enough trouble that it doesn't matter.

Cyberlimb joints would be more of a concern in my mind, and would need to be protected, and probably have heating pads around them to keep them from transferring the ambient cold and wind chill to the body directly. (Yeah, anyone that tells you that wind chill doesn't affect machines is talking out their hoop. Winnipeg just had a very nice example of that with our brand new parking meters.).

As for the rest, depends on the person's ability to handle cold (Which varies from person-to-person) and their current adaptation to the weather they're used to. If they just flew in from Jamaica, they're in for one hell of a shock. If they just flew in from Northern Ontario or Winnipeg, not so bad.

I really don't think it would matter. I've never known anybody with metal in their body (be those reconstructive plates or heavy gauge piercings) to complain about the effects of heat or cold; air just doesn't warm up metal that much. Getting into hot or cold WATER when you have heavy gauge piercings is a little bit annoying, because there's a lot more heat conduction going on.
Extremely cold weather might be an issue for cyberlimbs if they put a lot of metal in contact with flesh (which I kinda doubt they would - bu 205X they've surely got materials better suited to the purpose). Then again, cyberlimbs could be covered by the same clothing that protects flesh, and clothing in Shadowrun can easily be purchased with heating elements built in.

Honestly, I think unless you are an adept with temperature tolerance, your meat body will usually feel discomfort long before your artificial parts start bugging you. It's one of those areas of GM discretion, though. It probably depends on where you fall on the distopian vs. transhumanistic scale.

Or if you've experienced a Canadian Winter or not.

Honestly, Siberians complain about wanting to go back to The Old Country to get warm!

I'd agree, any piece of 'ware that isn't bargain brand garbage is going to be designed to be able to handle at least the temperature extremes the human body can handle before malfunctioning. I do imagine cyberlimbs in particular are designed so that no exposed metal is touching flesh, so you don't have to worry about say sticking your hand into the oven, and the limb heating up to the point that it burns your shoulder.

If they can make 'ware that can adept to all the weird things the human body can do, they can design it to handle temperature variations.

If they are made from metal and not plastic or ceramics.

There's at least some non-metallic stuff in a cybereye. You don't make a lens out of metal, usually.

Any cyberlimb/eye/ear/etc will be made of multiple materials. Most of that will be plastic, ceramics, metal, and glass. (Likely in that order)