In the abstract, either parsing is possible, so one could say that the phrase is syntactically ambiguous.
The context, however, clearly favours the second interpretation. Those who provide information on road conditions are generally not in the business of telling people that they ought to travel to this or that place. In other words, they can be presumed to never 'advise travel'. It is not necessary for them to tell us that they are abstaining from advising travel on a particular road on a particular day (the first interpretation), because they are known to never issue any such advice. The second interpretation, that they advise us to abstain from travelling is the only one that is compatible with their role.
One could, however, imagine syntactically similar phrasings, where the other parsing would make more sense. Suppose that an instructor gives the students a list of materials they are required to read for each class meeting, and that for one particular date, the list says 'no reading required'. It would be more reasonable to interpret that as 'you are not required to read anything' than as 'you are required to not read anything'.