I'm assuming we are the same as the US, and therefor it is not illegal to keep serving. Its just the perogitive of the bars.
When in the morning?
In the U.S., clocks change at 2 am local time. In Spring, clocks spring forward from 1:59 am to 3 am; in Fall, clocks fall back from 1:59 am to 1 am. In the EU, clocks change at 1 am Universal Time. In Spring, clocks spring forward from 12:59 am to 2 am; in Fall, clocks fall back from 1:59 am to 1 am.
Nationwide, U.S. restaurants and bars have varied closing policies. In many states, liquor cannot be served after 2 a.m. But at 2 a.m. in the Fall, the time switches back one hour. So, can they serve for that additional hour in October? The official answer is that the bars do not close at 2 a.m. but actually at 1:59 a.m. So, they are already closed when the time changes from Daylight Saving Time into Standard Time. In practice however, many establishments stay open an extra hour in the Fall.
In the U.S., the changeover time was arbitrarily chosen to be 2 am, when most people are at home. This is practical and minimizes disruption. It is late enough to minimally affect bars and restaurants, and prevent the day from switching to yesterday (which would be confusing). It is early enough that the entire continental U.S. has switched by daybreak, and the changeover occurs before most early shift workers and early churchgoers (particularly on Easter).