Lets run the numbers on this, comparing a 70gr Barnes TSX against 30-30 and 44 mag.
22-250 Muzzle 3,200fps and 1,591fpe
100 yards 2,962fps and 1,363fpe
(I wasent able to find barnes load data for their 70gr bullet for the 22-250 so I used reloading software to come up with the data, should be real close)
30-30 Muzzle 2,390fps and 1,902fpe
100 yards 1,975fps and 1,298fpe
44 Rem mag (rifle) Muzzle 1,760fps and 1,651fps
100 yards 1,425fps and 1,080fpe
Using that data seems that load for a 22-250 would be more than adequte for deer out to at least 100 yards, after all it carries the same energy that a 30-30 does, and Im sure most people think a 30-30 is more than enough for deer. And I know for a fact that a 70gr TSX will out penetrate a 30-30