Remember you might not see any copper at all, because diagonal cutters tend to drag the surface down along for the ride. A tinned copper wire tends to look silver on the cut ends unless you take the trouble to file/sand/grind down the end.
Like, here's a probably somewhat exceptional case. Biggest glass body diode I have, 1N4742A (possibly JAN?). Feels like nice soft copper leads. Magnetic. Probably nickel plated then.
Wait... the...hell?
Well, see for yourself;
31.5 mil (0.80 mm) o.d., apparently solder/tin plated copper OVER A STEEL CORE.
I can't say I've seen that before.
So you know how there's arguments where, some people say it's always X, and the other people say it's always Y... well apparently, sometimes it's X and Y.
I doubt this is by any means a typical construction, but it shows they weren't always just one or the other.
Other diodes: DO-201 style (rectifier and zener/TVS types) seem to fit with, oh hey, this datasheet gives composition, cool:
http://www.centralsemi.com/PDFs/case/DO-201PD.pdf1N914/4148 seem to be tinned steel, magnetic, as well as other DO-34 rectifiers and zeners.
1N2805A (50W 7.5V zener, TO-3 package) is heavy and nonmagnetic; seems to be plated copper, of all things. TO-3 are usually assembled by spot welding the top cover to the base, but that's only possible with steel; this one must be soldered, which seems unusual, but is probably quite reasonable for something as robust as a diode. Die attach might be solder as well. (Die attach in the above datasheet is claimed to be nearly pure lead.) Leads are apparently gold plated steel (magnetic, quite stiff), presumably with an underplating of copper (for adhesion) then nickel (diffusion barrier). (No, nickel plating wouldn't account for the attraction.)
Tim