Can senior NCO’s make soldiers drive from home to a duty during harsh conditions such as frozen roads?

It's your turn it's your turn. How much do you hate it when you get same day notice of a 24 hr duty? Now make it soley because you live in the barracks. That's messed up. That's why joe makes horrible marriage decisions to get out of the barracks. You wouldn't give those icy roads a second thought to drive 15 minutes to bang your favorite porn star, but you need to get to work and all of a sudden it's holy risk assessment batman!

It isn't a regulation it's the law - the UCMJ. It is an offense for you to be absent from duty without leave. The law makes no allowance for weather.
So, legally, yes. You can be required to travel through dangerous conditions to report for duty. Your authority to live off base will necessarily be conditioned on your being available on time. If you are supposed to be on duty and you fail to report without permission (regardless of the reason) you are AWOL.
Now for the reality check. What you ought to do if you are at home off post and you believe that travelling would be dangerous, call your PSG, TL or whomever you answer to. Let them know LONG BEFORE you are required to be on duty or as soon as you discover you will not be able to make it in on time. Let them know the situation with as much lead time as possible so they can sort out a replacement for you if necessary.
Any NCO worth his salt will take extenuating circumstances into account so long as you do not have a history of malingering or being a discipline problem. Adjustments can be made so long as they have time to do so especially as they need to let the COC know if they have given you permission to either miss duty or report late.
Best solution: if you see the weather turning bad and you suspect that it may interfere with your ability to report on time, grab your A & B bags and go to your unit while you can. Bed down there while weather is still permitting. It may be a pain in the ass but you should score some major brownie points for taking initiative and being reliable. You will also avoid pissing off your boss -- which is always a good thing.

Does the enemy stop when the weather gets scary? Is it fair to the soldier that lives closer to duty location to pull someone's duty that does not live so close? As a leader I would suggest to the soldier that is concerned about driving in weather to see if someone lives closer would be willing to switch. Each soldier made decisions on where to live and that does not change duty requirements. I drove 90 miles in snow and rain today because of my paramedic job. People still need help and I am the one that chose this profession. The only regulation that exists in regard to your question is command authority, nothing is written that automatically gets you out of duty in bad weather.

Bluntly, Yes. It was their choice to live off-post, if it is their turn at duty, then its their turn. You know that they have the right to move him into the barracks unless married and even if married they can move him temporarily into the billets as punishment or to ensure that the SM is present for duty on time.

Are you seriously asking for guidance on pawning off standing duty to the guys in the barracks because you have to drive 15 minutes? Do you not realize that is a morale killer?
If you are on the duty roster you know when and where you are supposed to be well in advance. Make the necessary arrangements, even if that includes getting up and going in earlier. Don't expect someone else to cover for you.
You made a decision that led you to living off post, whether it was marriage or something else. You must accept the responsibility that goes along with it. I bet most of the guys & gals in the barracks would kill to move off post, even if it meant driving a few miles in bad weather every now and then.

Road conditions suck, it is your day for the duty, get up earlier, or call to let them know you are heading slow as the road conditions are poor. Thinking some one who lives closer should pull your duty...be thankful you are in now and not 20-40 years ago, your team mates would have had a conex counseling session with you.

You have a duty on a specific date and time you are expected to be there. No there is no regulation to what you speak or are seeking. Command can make exceptions but we are all grownups and expected to be aware of the hazards and how to mitigate them to be where we are supposed to be.

The military did not issue us wives and families. We chose those.

There's several things to consider.
-First, it's your choice to live off base. You're expected to show up for duty at the appointed time with the correct uniform and equipment. Leave early!
-A fifteen minute commute doesn't seem very long.
-The Base might be closed except to mission essential personnel due to weather. The essentiality of your duty is up to your supervisor. Be sure to check the installation web page where closure information is often posted. Also check with your supervisor.
-Scheduling people for duty based on their marital status, age, rank (in some cases), residence location, and many other things is a rabbit hole most supervisors don't want to go down. There's no bottom and they could end up with an EO complaint.
-If you sincerely believe it is unsafe for you to attempt to travel to the base, or if law enforcement has closed roads between your home and the base, you should contact your supervisor immediately.

Think about this you fail to show up for duty some one else my not be able to go home, not cool

My former.commander ordered me to come in during a snow storm, I ended up hitting black ice and rolling my truck, lucky for me. I wasn't badly injured .Even good commanders make bad decisons.