Really depends on how hard it is.
A true cupro-nickle jacket will be a solid alloy of copper with some nickle and some iron. It's the same material through the entire jacket. If the jacket only has a thin layer of copper alloy on the outside and a solid mild steel layer it would normally be called a bimetal jacket with cupro-nickle instead of copper plating.
The copper or cupro-nickle plating on bimetal jacketed ammo is very thin. This cross section shows a typical example (different manufacturers will be different):
http://infothread.org/Weapons and Military/Bullets/Wolf .308 bi-metal.png
If a magnet sticks as strongly as to Soviet 7.62x39 or x54R surplus, it's probably a bimetal jacket. If it sticks very weakly it could be a solid cupro-nickle jacket with some iron in the alloy. The former would be harder on the barrel and the latter would be easier.
There's a good article to read about mild steel jacketed ammo versus copper jacketed here:
http://www.luckygunner.com/labs/brass-vs-steel-cased-ammo/
The article is technically about steel versus brass cased ammo but there is far more information on the differences between bimetal bullet jackets versus copper bullet jackets.
Is it good for the rifle? No, but neither is copper jacketed ammo. Any ammo will eventually wear out the barrel, it's just a matter of when. In the test from the article above the bimetal jacketed ammo killed the barrel in around 6000rnds, the copper jacketed they guessed would have done the same in around 12,000 rounds (they only tested to 10,000). Of course that is 223/5.56 and we're talking about 7.5x55 so pressures, velocities, bearing surfaces, etc. are all different. I'd use the results of the article more as a rough guideline than an absolute answer. Accuracy will get worse as it wears out more so a match barrel might be pooched for match-grade accuracy after only a couple thousand rounds. It'll still shoot but accuracy will get progressively worse.
Unless you have a few thousand rounds with steel jackets and will be putting them through the rifle in your lifetime, I wouldn't worry. Personally unless it's a collectors grade high dollar value rifle, I'd just shoot the bimetal ammo. Replacing a barrel will cost quite a bit less than buying new commercial ammo with copper jackets. If it's a high dollar rifle with a matching barrel I wouldn't shoot it much at all with any type of ammo.