Hi,
From my point of view, if the Alternate airport is closed at your ETA at destination, we CANNOT nominate it as an alternate as it will not be available for diversion should it be necessary. Further more, as per SOPs, the alternate airport availability is checked for the period ETA (alternate) +- 1 hour.
Of course, there is an option to dispatch without an ALTN. A dispensation from various authorities is needed should it be necessary to dispatch a flight without an ALTERNATE and of course we top it up with as much fuel as possible and the weather is excellent.
My 1 cent worth,
Cheers