I have been told the hut closes that time of year due to opperating costs more than anything else. Plus it gives them enough time to properly secure it for winter so they can drain lines, board up, clean etc before full on winter.
But, it is safe to hike this time of year as long as you:
1. look at the weather report before going. If it is forecasted to be 20F blowing 80 mph and all you have are tennis shoes and a sweat shirt, then no, it might not be the brightest thing to do. Also, asses the weather as you go. We forecast the weather but no forecast is written in stone. If the weather is turning bad, make the correct decision to turn back down. Once you are above treeline, you are exposed to whatever is going on with little protection.
2. hike with a friend. Even the most experienced people will tell you it is safer to hike in pairs than alone. And even then, check in or let others know your plans.
3. start early. days are getting shorter so the sooner you start off the more time you have to play with.
4. If you hike up, plan to hike DOWN. This time of year, there is no guarantee that there will be a ride down. This is true at any point in the summer but this time of year with icing starting, the cog and autoroad stop running in bad weather. And for rides down, the cog goes one way and the road the other so if only one is running down, you might be taken 50+ miles away from where you need to be.
5. Avoid anything cotton. cotton does not breath and it does not dry for a long time. and pack plenty of layers. it might be 60-70F in the valley but it might be 20-30F up top.
6. don't be ashamed to turn around. the mountain is surprisingly deceptive. it might seem like you are close to the top but it is usually an optical illusion. I can't tell you how many rescues or hypo cases we have had where they said they thought they were close to the top so they pushed on growing more cold rather than heading down where better weather lies. The mountain will be there another day. Just because you planned to hike on x day three months ahead does not mean you have to hike on x day when it arrives.
These are some of the key things that come to mind. I am sure others can feed in. But don't let us deter you from going. Just be prepared and heed any advise given so I or anyone else does not have to rescue you. Shoulder seasons (spring/fall) have the most recues due to niave thinking and unpreparedness.
Staff Meteorologist/Night Observer, KMWN (Mt Washington Obs., NH)