357 Mag Rifle (From
http://www.hodgdon.com/)
150 GR. NOS JFP 150 H110 .357" 1.590" 16.0 1766 23,600 CUP
Max
150 GR. NOS JFP 150 H110 .357" 1.590" 17.0 1807 28,900 CUP
For comparison 44-40 Rifle
200 GR. LEAD RNFP 200 Titegroup .428" 1.600" 5.0 956 8,400 PSI
Max
200 GR. LEAD RNFP 200 Titegroup .428" 1.600" 6.2 1117 12,900 PSI
30-30 Win
170 GR. SIE FP 170 BL-C(2) .308" 2.550" 32.5 2048 27,900 CUP
Max
170 GR. SIE FP 170 BL-C(2) .308" 2.550" 36.0 2227 34,700 CUP
The max loads above are near Sammi max loads, and listed as max loads by Hogdon
So yes, the 357 Mag would make a decent short range deer cartridge. I'd want to study it's down range performance before shooting much over 100 yards though.
My experience with "Max" indicates that with some rifles, and some cartridges, (the 44-40 is a perfect example) 'Max' is a joke. However, max was designed to keep older rifles that may have problems, and their owners, in one piece. You're on your own if you push the limits.
My experience with the 44-40, at least in my rifle, is that it doesn't have the twist rate to stabilize bullets much faster than 'max' and accuracy suffers