The word "supposed" is an interesting one. What part of speech is it? In my opinion, it is part of a passive voice construction in the present tense. One supposes things, concepts, and even people. In this case "We are supposed" means that others are supposing us to be doing something. It has taken on the meaning of obligation. The verb suppose takes an infinitive. We are supposed to be skiing. "To be skiing" is the progressive infinitve of "to ski" -- "to be skiing".
I am skiing.
You are skiing.
He/she/it is skiing.
In the "to go skiing" form, either "to go" is an infinitive and skiing is a gerund object of the infinitive, or "to go skiing" is a phrasal infinitive with "go" acting as a helping verb. I prefer the second explanation, but most dictionaries give that use of "go" as a transitive use, requiring a direct object. I think either explanation is acceptable.
When “To be” verbs are combined with modal forms in this manner, the construction is called a phrasal modal. Here are some more examples:
Rosario was able to finish her degree by taking online courses.
She wasn't supposed to graduate until next year.
She will be allowed to participate in commencement, though.
She is about to apply to several graduate programs.
She is going to attend the state university next fall.
Sometimes it is difficult to say whether a “To be” verb is linking a subject to a participle or if the verb and participle are part of a passive construction.
In “Certain behaviors are allowed,” is "are” linking “behaviors” to "allowed" (a participle acting as a predicate adjective) or is “are allowed” a passive verb? In the final analysis, it probably doesn't matter, but the distinction leads to some interesting variations. Consider the difference between
The jurists were welcomed.
The jurists were welcome.
In the first sentence, the participle “welcomed” (in this passive construction) emphasizes the action of welcoming: the smiles, the hearty greetings, the slaps on the back. In the second sentence, the predicate adjective “welcome” describes the feeling that the jurists must have had upon being so welcomed.