This is a matter of formal agreement versus notional agreement.
Formal agreement is the strictly grammatical agreement between the verb and the subject: a singular subject must be matched by a singular verb.
Notional agreement is more flexible, and allows the verb to matched to the idea - notion- of the subject. For example
"The board of directors is in agreement"
"The board of directors are arguing"
In the first, the notion is unity so a singular verb is appropriate, in the second the notion is disunity so a plural verb is used.
This works when the individuals and the collective are the same thing. 'The Board' and 'the directors' have the same referent. They are the same idea- the same thing. In your example 'the pack' and 'the wolves' are the same thing. This contrasts with, say, 'the bag of footballs' in which the 'the bag' and 'the footballs' are entirely different things.
As a native BE speaker, I would say that notional agreement is more usual in BE. Sometimes we treat groups as singular and sometimes as plural. Text books often say that formal agreement is more usual in AE, but I am not entirely convinced.
Getting around to your wolf pack, I would say:
"A pack of wolves runs through the woods."
because they run in unison. If they stopped to eat I would change:
"A pack of wolves eat [or "are eating"] in the woods"
because eating is an individual activity.
If somebody else said "A pack of wolves run through the woods" I wouldn't say it was wrong. It is just different.