The receiver and bolt on a M1903A3 is made from 8620, which is a good alloy steel, and these rifles were made in a time when metallurgy was a mature science. A M1903A3 will be stronger than any of the single heat treat or double heat treat M1903's just due to the metal technology. None of the 03's actions handle gas worth a flip, so don't load the thing so hot that either the primer pierces or the case head blows. With these, always wear shooting glasses because hot gases vent directly down the firing pin shaft into your eye!
I have shot thousands of rounds in local club competitions in my M1903a3's, I can recommend a load that is close to the service rifle load:
150 grain bullet, 47.5 grains IMR 4895, any case, any primer.
An excellent target load is a 168 Match, 47.0 grains IMR 4895, any case, any primer.
I do recommend you buy the 20 lb Wolff mainspring and replace whatever vintage mainspring is in the rifle. Of the military actions on the market, for whatever reason, M1903 mainsprings take a set and provide rather asthmatic performance. A new mainspring will improve ignition and crispen the trigger pull.