The original reason for playing the paleface attack
1.d5 Nf6 2.f3 was to transpose into the BDG after 

2...d5 3. e4 dxe 4.Nc3 avoiding the Huebsch gambit 

1. d4 Nf6 2. Nc3 d5 3.e4 Nxe4

However black can play 3.e6 in either of the above lines.

Gunderam analysed

1. d4 Nf6 2.f3 d5 3.g4

Hmm, I didn't seriously consider 5.g4.  But after 5...Qh4+ 6.Nf2 I don't see anything convincing yet.  It's hard to believe such a move actually works!

Maybe black should try
4.Nh3 Bc5 5.e3 d6 and if 6.g4, then 6...Qh4+ 7.Nf2 Nf4.

But then again 5.e3 isn't forced, so probably 5.Bg5 is more cause for concern.  I don't see a good answer to this.

So maybe black should try 4...d5 intending

5.g4 Qh4+ 6.Nf2 Bc5 7.e3 Nf4
5.Bg5 f6 (OK I think this is the best but I don't think I like it for black)  6.exf6 Nxf6 (6...Bxh3 fails to fxg7 and 6...exf6 fails to Qd4 followed by Qh4) 7.Nf2 Bc5 and black may have enough compensation, but I have my doubts.

So maybe 2...e5 is busted!

4.Nh3 might be better than 4.g3, though

1.d4 Nf6 2.f3 e5 3.dxe5 Nh5 4.Nh3 d6 5.g3 Nd7 (5...dxe5 fails to 6.Qxd8 Kxd8 7.Ng5) 6.exd6 Bxd6

might give black good compensation simliar to the lines after 4.g3.

In the line
1.d4 Nf6 2.f3 e5 3.dxe5 Nh5 4.g3 (If my earlier analysis is correct, then it may be best to prevent Qh4+ with 4.g3.)

I think 4...d6 is best (instead of my earlier suggestion of 4...Bc5) since it takes immediate action against white's center.

For example, after

4.g3 Bc5 5.Nc3 Nc6 6.Ne4 Bb6 7.f4
white seems to be consolidating and may have the advantage.  For example, the direct attempt to break with 7...h6 is met by 8.e3 attacking the now awkwardly placed knight on h5.

However, I think 4...d6 is very convincing:

4.g3 d6 5.exd6 Bxd6 is very dangerous for white with the threat Nxg3 looming:  
6.Kf2?? Bxg3+
6.f4 Bg4 is very loose
6.e3 is probably best, but 6...0-0 7.Bg2 Qe7 8.Ne2 Rd8 would make me very nervous.

If 5.e4 (which I think is better) then 5...dxe5 6.Qxd8 Kxd8 is fine for black (and probably best), though black may have more with 5...Nd7!?:

6.f4 g6 7.exd6 Bxd6 8.Nf3 0-0 9.Be3 (9.Be2 Qe7 10.e5 Bc5) 9...Qe7 10.e5 (10.Bd3 Nhf6 11.e5 Nxe5!! 12.fxe4 Bxe5 13.Nxe5 Qxe5 14.Qd2 Re8 15.Ke2 Ng4 wins!) 10...Nxe5!? (!!, maybe?) 11.fxe5 Bxe5 12.Nxe5 Qxe5 13.Qd2 Bg4 with a dangerous initiative.

I haven't checked this carefully, but the Nxe5 idea seems interesting!  It seems like black has good compensation for the pawn.

Is 2...e5 the refutation of the "Paleface Attack"?

Who named this the "Paleface" and why?  It sounds like someone joked about having a "pale face" after seeing their opponent play 2.f3.  ("Oh no!  He's gonna play the Blackmar-Diemer!")

After 1.d4 Nf6 2.f3 d5 probably the best white can hope for is an inferior line of the Veresov.  OK so 2...d5 is obviously good for black.  When I see a move like 2.f3, I start to look for absurd moves and see if they are playable.  So let the sillyness begin!

I)2...c5
2.f3 c5 3.d5 e6 4.c4?!
White now thinks he's going to play a Half-Samisch Benoni.  A transpositional victory for the "Paleface"?

[4.Nc3 is probably better but 4...exd5 5.Nxd5 Nxd5 6.Qxd5 d6 looks like an improved anti-Benoni line for black.

After 4.e4,  4...exd5 5.exd5 (5.e5? Nh5 6.Qxd5 Qh4+) 5...Qe7+ 6. Ne2 (6.Be2 Nh5) looks awkward for white, but 4....Nxe4 looks tempting (though it's probably not that good).]

4...exd5 5.cxd5 Nh5 6. g3 Bd6 and 7.Kf2 is probably white's best move.

II) 2...e5!?
This is the absurd response I was thinking about.  It actually may be good!

2.f3 e5!? 3.dxe5

[3.d5 Bc5 is excellent for black; 

3.e4 Nxe4!? 4.fxe4 Qh4+ 5. Kd2 cxd4 looks dangerous (Well, it probably doesn't amount to much after 6.Nf3 Qxe4 7.Qe1.), though after 3...cxd4 4.Qxd4 Nc6 black is already better.]

3...Nh5 4. Be3 (4.g3 Bc5 has to be good for black.) 4...Qh4+!? ("This is crazy, this is crazy!") 5.g3 (5.Bf2 Qb4+ 6. Nd2 Qxb2 looks all right for black.) 5...Nxg3!? 6.Bf2 Qb4+ (the point!?) 7.c3 Qxb2 8.Bxg3 Qxa1 9.Qb3 d6 10.exd6 Be6 11.Qxb7 Bxd6 12.Bxd6 cxd6 13.Qxa8 Qxb1+ 14. Kf2 0-0 and black is better!

Okay, that's long (and probably wrong), but one thing came up after another and I couldn't resist!  I would like to see an attempt at refutation (which may be easy ).  The same goes for the analysis of my Benoni 7.f4 Qe7!? post.

I was of the opinion that this was a move order commonly used by BDG players.  Anyway,  Black could certainly transpose to King's Indian, Benoni, or Pirc positions.