It gets plenty cold here in Santa Fe too, but there are still many, many to choose from. A good southern exposure, like up against the winter sun side of your house, helps a great deal in growing the more tender ones. I grow the following cacti and succulents (in no particular order), and I've only scratched the surface. They provide a year-round interest of unique shapes, colors, flowers, and fruit:

HEDGEHOG CACTI
claret cup (Echinocereus triglochidiatus)
scarlet beehive (E. coccineus)
Fendler's hedgehog (E. fendleri)
strawpile hedgehog (E. stramineus)
Engelmann's hedgehog (E. engelmanni)
green-flowered hedgehog (E. viridiflorus)

PRICKLY PEARS
NM prickly pear (Opuntia phaeacantha)
spineless prickly pear (O. ellisiana)
Engelmann's prickly pear (O. engelmanni)
plains prickly pear (O. polyacantha)
bigroot prickly pear (O. macrorhiza)
long-spined prickly pear (O. macrocentra)
Santa Rita prickly pear (O. violacea)

CHOLLAS
cane cholla (Cylindropuntia imbricata)
christmas cholla (C. leptocaulis)
Klein's cholla (C. kleini)
dagger cholla (Grusonia clavata)

OTHER CACTI
AZ barrel cactus (Ferrocactus wislizenii)

AGAVES
Parry's agave (Agave parryi)
Havard's agave (A. havardiana)
desert agave (A. deserti)

YUCCAS
plains yucca (Yucca glauca)
Whipple's yucca (Y. whipplei)
soaptree yucca (Y. elata)