Assuming you mean a 7x57mm Mauser which is the most common 7mm rifle cartridge as apposed to a 7mm Mag. The 7x57mm with a 173gr round was lighter than the .30-06 with less powder space and was the original bolt action cartridge at the turn of the century. In the Spanish American wars in Cuba the Spaniards out ranged our boys using .30-40 Krags, which was the precursor to the .30 caliber rimless case redesign in 1906 as the standard U.S. Military round hence the .30-06 designation. The Springfield 03A3 rifles were designed as bolt action rifles patterned after the Mauser action rifle.
So a if you shot a 7x57mm than the recoil is similar but less than the .30-06 with a 150gr bullet load. The 180gr loads in the .30-06 would be a higher but not bad compared to a belted magnum such as the 7mm Mag.
Many troops in the Cuban campaign still carried .45-70 Springfield Trapdoors. In between the .30-40 and the .30-06 was the very short lived .30-03.