I'll weigh in on which way this case will go. I am a second year law student (in the states) and am currently taking trademarks.
If 123ski's post is correct, i think WME will have some difficultly litigating the case, but it may go either way. NOTE - the complaint does not allege a violation of Miller's exclusive licensing arrangement. The case appears to be solely one of trademark infringement.
The burden is on WME to establish, firstly, that a TM exists in warren Miller's voice. They would seem to have an argument here. They have been using miller's voice exclusively and the public has come to associate the voice of miller with the films - elements for finding a mark (among others) but more facts are needed. Luckily it does not appear that a mark is registered on miller's voice, therefore WME will have the expensive and fun time of establishing that the mark exists
An aim of trademark law is to protect the public from confusion. The harder argument WME will have to make is that the public will be confused by warren miller's voice in the film. Confusion exists in two forms - pre and post sale.
1. Presale confusion is confusion of origin leading the consumer to purchase the product believing it originates from another company - WME. It does not appear that miller's name is on the packaging of the movie. The packaging does not state - Warren Miller: Refresh for example. His name may be on the box credits but this would not likely be found by a court to mislead given its less than prominent placement. Moreover, L1 did not advertise tickets for ANY of its shows mentioning miller in the film. in fact, miller's involvement came as a complete surprise to most in the ski scene. Thus, there would likely be no confusion found in relation to ticket sales. I think L1 has a good defense on this argument.
2. Post sale confusion occurs when people other than the purchaser are confused as to product origin. The argument here (which they may not have made at all) would be that people watching the movie, at home for example, would watch the film and be confused - believing that it originates from WME. I'm unsure about this argument but it is compelling at first glance.
Legal arguments aside, the big problem is that WME has a fortune available to pay legal fees with. L1 Does not. Thus, WME can simply continue the litigation, increasing costs, and forcing L1 to settle simple because they cannot afford to litigate any longer - this happens often with small companies.