Wa'ant no .30-06 in Cuba in 1899.
The Rough Riders' '95s would surely have been in .30 Army = .30-40 Krag. The '95 Winchester, a Browning design, as usual, had a single stack box magazine in front of the triggerguard. They were made in .38-72 and .40-72 blackpowder calibers when they first came out, but were soon updated to .30-40, .303 British, .35 Winchester, .405 Winchester, .30-03, and .30-06 smokeless calibers. By far the most '95s were in 7.62x54R and went to Russia. Some were reimported in the last years of mailorder milsurp in the 1960s.
The current lot of Winchester/Miroku repros is in .405 and Hornady is making the ammo. A 300 grain bullet at 2250 fps or thereabouts. You can find .30-06, .30-40 and even .270! M95 repros on the second hand market.