The verb ist is 3rd person singular, which is the form that always occurs when the verb has no subject argument.
Ist Ihnen heiß, schwindelig, schlecht?
Are you hot, dizzy, sick?
In the above example, heiß, schwindelig, schlecht are adjectives that occur together with a dative, i.e. Ihnen. Verbs never agree with a dative, so even if Ihnen is plural, the verb is 3rd person singular as there is no subject present. Your assumption that the form ist is independent of euch is correct.
Another example of verbs missing a subject argument is impersonal passives, where the verb occurs in the 3rd person singular as well.
Wurde euch geholfen?
Ihnen wurde nicht geglaubt.
As far as meaning is concerned, you can treat
Mir ist (nicht) nach …
as an idiom meaning
I (don't) feel like …
The preposition nach can probably be explained by deriving the idiom from zumute sein nach.
Ihnen war nicht nach Feiern zumute.
They didn't feel like partying.