No, you can only use Intimidate when trying to get a hunch or detect if someone is trustworthy or not.
Sense Motive in Snake Style is not a standard use of Sense Motive, so no.
the skill sense motive only has three options listed: hunch, sense enchantment, and discern secret message. the snake style feat does not say there is now a forth option it simply says make a sense motive check. of the three options available within the sense motive subtypes hunch makes the most sense as it talks about gut instincts.
Terrifying Mask: "Anytime you can make a Sense Motive check to get a hunch or detect whether someone is trustworthy or not, you can choose to..."
Snake Style (Combat, Style): "While using the Snake Style feat, when an opponent targets you with a melee or ranged attack, you can spend an immediate action to make a Sense Motive check. You can use the result as your AC or touch AC against that attack."
When using Snake Style, you are not making a gut assessment of the social situation, nor are you trying to get the feeling from another's behavior that something is wrong. Doing so (the "Hunch" task) has a set DC, and generally takes at least 1 minute. Since that's not what you're doing, Terrifying Mask does not apply.
the snake style feat does not say there is now a forth option
Uh, yeah, that's exactly what the feat does. How could you interpret it any other way?
the skill sense motive only has three options listed: hunch, sense enchantment, and discern secret message. the snake style feat does not say there is now a forth option it simply says make a sense motive check. of the three options available within the sense motive subtypes hunch makes the most sense as it talks about gut instincts.
Does is specifically say it uses the hunch? Then you do not know that it does. It simply uses the Sense Motive skill as a measure of how well you can read the body language of the target to tell where, when, and how he will attack. That's not a hunch, and the mechanics are not the same as a hunch as Grick rightly points out.
Now if you can point out how using Intimidate allows you to read body language or otherwise understand how and in what way somebody could attack you, I'm all ears, but I don't see it myself.
If a character has invested in Intimidate instead of Sense Motive, then Snake Style is clearly not for them, mask or no mask.
Honestly, the RAW says no, but the concept is awfully cool.
Snake Style is normally about reading body language to preemptively learn where a strike is about to come from and dodge it.
The Snake Style/Terrifying Mask combination is about scaring someone so bad that they flinch mid-strike and miss.
That's pretty neat. I'd probably allow it.
Snake Style still has the Sense Motive prerequisite, so the skill point tax on the feat would have to be paid normally. This just opens up another way of doing something the character would already be able to do.
Another way of looking at it is that the character is taking a feat that reads "When using Snake Style, you may use your Charisma instead of your Wisdom when making Sense Motive checks".
That seems like a perfectly reasonable use of a feat to me.