Alert! Heavily simplistic answer incoming!
Depends largely on three things.
1) How well Rose plays between now and January.
2) How well Ade comes on between now and January: i.e, will he turn out to be a good option off the bench?
3) How well BAE plays at QPR between now and January: i.e, is it worthwhile recalling him to be Rose's back-up/replacement in the starting eleven?
If the answers to all the above are negative, i.e Rose plays badly/stays injured, Ade fails to impress and BAE struggles at QPR, then we'll need a left-back and a striker. Luke Shaw and Javier Hernandez, please: around 20 million for the first and about 15 million for the second (Hernandez will probably be more expensive to us than he would to other clubs due to our snubbing of United's Bale/Modric advances, but we should try anyway). Depends heavily on whether we can sell Ade and BAE (
) for something approaching a decent price (say, 5 million each) and if we can shift a few of our players on loan to clubs that would play them regularly (Mason, Coulibaly and the like: NOT Carroll or Pritchard). If we can garner some sixteen million in sales in the window, then we'll have a net spend of minus 20 million quid counting the summer, which should help us justify spending 35 million quid to ourselves (because it enables us to stay below or around our average net spend of 16 million a season). It will involve paying high wages to Shaw (Chelsea fan, after all, and seems content at Southampton, so big incentive needed to move) and Hernandez (again, seems content at United despite getting almost no chances to play), but the savings on Ade's wages should help offset that cost.
Shaw and Hernandez. Problem sorted.
Of course, if Rose ends up impressing and BAE gains enough fitness to be recalled as cover, then we won't need a new left-back. Similarly, if Ade grasps what I suspect may be his last chance to impress, then we won't need a striker either. In that case, though, I'd still like to see us try for Shaw, perhaps with a view to loaning him back to Southampton until the season ends. He will be England's next left-back for many years to come, and we need to start bring up our English quotient a wee bit. We also will likely need another left-back (seeing as AVB doesn't seem that keen on BAE), so the move makes sense: two high-quality English left-backs fighting over the position should help our squad depth to no end, whoever turns out to be the victor.