Frostburn damage and Regeneration.

[ksbsnowowl]

Unlike normal damage, however, frostburn damage does not heal naturally and may only be healed magically with a successful DC 25 caster level check as long as the victim remains in cold or colder temperatures. If the victim reaches an area of moderate or warmer temperature, his frostburn damage becomes normal damage that can then be healed naturally or magically in the usual manner.

How does this type of damage interact with Regeneration?

[X-Codes]

Regeneration converts all damage that doesn't bypass it into non-lethal damage, and then heals said damage... so I'd say the Frostburn effect only takes place if your Regeneration is bypassed by Cold damage (note that Trolls do like cold climates...).