No, although perhaps we should....
I have never heard of a spencer.
We do have long sleeved thermal underwear of various fabrics available - everything from silk to cotton thermal to smart wool to gear-type moisture wicking manmade fabrics.
But speaking personally I never wear that sort of thing except for gear-type outdoor activity.
I would more likely layer a camisole or tank, woven shirt, jacket (and coat, if necessary). Or I'd wear a knit layering T with a jacket and scarf.
Do people commonly wear these in Australia, Anne? It's so interesting to me. I wonder where the name came from.