The best would be to run a fiber cable between the house and the home office, with media converters on either end, and then you wire the house end to your router. If you have contractors already doing work on building the office, maybe installing the cabling could be added on to the existing project?
Alernately, 55m is not a terribly long distance, so a wifi bridge would also work - assuming you have clear line of sight between the house and the new office.
If I understood right, you’re downgrading your connection from 500 to 70Mbps, and the question is whether this will be enough for six people?
I’d say it depends on to what degree all six of you will be doing bandwith intensive things at the same time.
For example, Netflix recommends minimum 15Mpbs for a 4k stream, so if all six of you will be doing that on separate screens at the same time, you’ll be about 20Mpbs short. But if everyone is on 1080 screens you’ll be fine as the requirement is 5Mpbs per stream.
Remote work doesn’t necessarily require a lot of bandwidth, although it depends on what you actually do for work. MS Teams for example only requires about 2Mpbs for group video calls.
Most gaming also doesn’t require a lot of bandwidth, but of course downloading games and their updates does.
Will it work? Yes I think so, though you may encounter times when it gets laggy.
If you’re not messing with it (as in, trying to move/bend the cable when it’s icy cold), I don’t think winter is the main issue. I think the main problem with having cables like this outdoors is UV (sunlight) breaking them down, causing the cable jacket to crack, and then you get water ingress. Like in the video here: https://www.reddit.com/r/IndianGaming/comments/lt3u5v/water_droping_from_my_ethernet_cable_i_noticed/
I would replace the outdoor sections of the cable with one that is actually rated for outdoor use, but it will probably be fine to wait until the spring/summer.
If the extender is just gathering dust anyway, I would just try it. It’s not rated for freezing or very hot weather, but I don’t think neither the cold or hot weather will really damage it as long as it is inside the garage, protected from rain etc. No guarantees though.
Or pick up the cheapest wifi repeater you can find and use that.