The way I read the question.....the aircraft has not departed base yet.
My answer would be to determine when the flight could be made after frontal passage and weather within minimums could be expected, provide the estimated time, advise the tasking authority of that and remark I would monitor the weather and report being able to make the flight as soon as I could.
If the question meant an enroute situation.....it is arrange ground transport and meet that unit at the nearest point to the destination possible or divert to the nearest best medical facility and wait for ground transport there.
Continuing on in deteriorating weather below minimums is not an option.
People are going to die.....all you can do is your best....and go home at the end of your shift to fight with the wife and beat the kids....I mean fuss with the kids and beat the wife.