This will only impact those publications using the default folder. This can be changed in subscription settings.
Note that the service account for the Snapshot Agent MUST have read/write permissions to the new location, the Merge Agent or Distribution agent needs read permissions to the new location, and that you need to re-create any sharing settings for pulled subscriptions on the new location.
Note that the distribution cleanup agent will NOT clean up the snapshots in the old folder location. Delete those at your leisure, when you are not going to need them to resync a new subscription.
To verify the change:
To view all snapshot agents and generate a script to start the job. Not recommended to do all at once, but it can be handy for servers with many publications.
select distinct j.name, tsql = 'exec msdb.dbo.sp_start_job ''' + j.name + ''''
from msdb.dbo.sysjobs j
inner join msdb.dbo.syscategories c on j.category_id = c.category_id
where c.name = 'REPL-Snapshot'
and j.enabled = 1