I'm not sure that 'thrive' is the word I would use. But palms surprise people ALL of the time. If you could take pictures, then those palms you've been seeing could be quickly identified.

Pindo Palm is Butia capitata, aka Jelly Palm. It is VERY common in warmer climates, but is still considered one of the semi-hardy palm species. Butia fronds are very long and arching, unlike so many others that are fan shaped.

You are likely to see winter injury where you are.

Here is a link that might be useful: {{gwi:578987}}

Yes, I definitely need to take pictures - didn't think about that. The plant I am trying to describe looks like the one you posted except they are taller (with more of a trunk) and on some the fronds reach almost to the ground.

Well........taller means OLDER ;-) I sent you that image so that you could see a good shot of the fronds. These (and all) palms start out very tiny, then spend many years developing a nice fat crown before they begin growing tall.

Here is a link that might be useful:

Palm trees that are completely hardy in the SC midlands include:
Windmill palm (Trachycarpus fortunei, T. takil)
Dwarf windmill palm (T. wagnerianus) All windmill palms like a bit of afternoon shade.

Palmetto palm (Sabal palmetto) Full sun

Palm trees that do ok, but can get damaged by severe winters include:
Mexican fan palm (Washingtinia robusta) Full sun
California fan palm (Washingtonia filifera) Full sun, massive trunk, this palm is several degrees cold hardier than the Mexican fan palm.

Pindo palm (Butia capitata, B.eriospatha) Full sun, edible fruit

Puerto Rican palmetto (Sabal causiarum) Full sun, massive trunk

Palm shrubs completely hardy in the SC midlands include:
Dwarf palmetto (sabal minor)
Mexican dwarf palmetto (Sabal tamaulepis)
Sun or shade

Needle palm (Rhapidophyllum hystrix) Part sun to shade

Palm shrubs that do ok, but can get damaged by severe winters include:

Saw palmetto (Serenoa repens)

Wow, thanks for the info. That is exactly what I was looking for. I had been interested in shrub type palms as well but I didn't know what I was looking for or at.

Now to get rid of that camellia in my front yard that is going to get a palm replacement. Any one want a 30+ year old camellia?