Is there a way to get vaccinated at home or is a booster for my mom (92) worth it?

Check with your county. Some will send a nurse to the door of homebound to administer the shot.

A boostered senior 65+ is 50 times less likely to be hospitalized for covid than an unvaccinated one. Most of those who progress to ICU are in fact seniors. Yes, the extra insurance of a boost is well worth it.

Blue states as well as red are removing indoor mask mandates. That plus Omicron means more chance of spread. Yes there is reason to worry about it, particularly for one so frail.

https://www.sccmo.org/2162/COVID-19-Vaccine-Information

I think this might be the link to your county health department. Give them a call and see if they are making house calls in cases like your moms.

It is also good for her to take Vitamin D3, Vit C and zinc. You can probably find a multi with those combined. This was recommended by my husbands cardio when he tested positive.

In the home medical services are incredibly beneficial well beyond covid vaccines, once it became difficult to get my mother out for appointments it was a real relief to me that I had access to a nurse and doctor.

AMD=Age related Macular Degeneration.

You will have to do a risk assessment for her. What is AMD? If your mom doesn't have the other concerning underlying conditions, like being immuno-compromised, obesity, COPD/asthma/breathing issues, CHF, HBP, diabetes, etc. (not a complete list) and has very little exposure to others, she will be at less risk, but there's still always a risk. Omicron is more virulent but far, far less deadly than original covid.

My 86-yr old MIL is in LTC in a facility. She got and then survived original covid in May 2020 (9 residents died). Eventually she got her Pfizer vaccine. Then Omicron blew through recently (residents were getting it from staff) but no one was hospitalized or died -- very mild. Within the past 3 months our church had 3 people pass from covid (and I don't know what variant they had). All were unvaccinated. Ages were 62, 72 and 48. All were overweight (but not what I would call morbidly obese), 2 were former smokers, one also was diabetic. They may have had other issues of which I'm not aware.

My own 92-yr old mom has had the first Pfizer vaccine and never had original covid (she may have had Omicron last month but didn't want to be tested) and she doesn't want the boosters. She still drives and has been going out in public almost every day to stores and only wearing a mask where required. Her only health issue is arthritis, so in spite of her age, she is low risk. She's a retired RN and has never liked taking "too many" medications, even for pain.

All this detail just to point out that having pre-existing or underlying conditions seems to be the most worrisome risk factor, not simply age or being underweight. I'm not saying she should or shouldn't get a booster, only that if none of the other health risks are present you can probably worry a little less.

Call your local Area Agency on Aging and find out if there is a home vaccination program in your state.

I would also be trying to find a doctor or nursing service that makes house calls. It sounds like your mom is much too frail to be going out, cold weather or not.