Janet, I can't really answer for the original poster, obviously. I don't have particularly weak arches, either, and don't normally wear an orthotic or anything like that, but when you are standing on hard floors for a long period of time (as with cooking, etc.) a sole that absorbs shocks can be important (esp. when dealing with plantar fasciitis, as I have been). So my own requirement is more for that than for arch support, but I can imagine how it might be for someone else.
Also, if you work from home, it's really what you are wearing all day, not "just around the house" -- I mean it's what you are wearing all day at work, so to speak.
And then -- while the idea of an "indoor shoe" vs. a slipper would seem to answer that particular issue (I mean, why not, right? No one says it has to be a slipper, per se; it can just be a shoe you don't wear outside!) -- but then you lose the "cozy" and "warm" factor really fast because most shoes are not designed to be cozy or warm (whereas slippers are.)
I think in your climate I would probably wear slip on sneakers in the house or something. I bring my fleece slippers out at some point in November and wear until the end of April or so, at which point I switch to slip on sneakers for a while, and finally a sandal.