My Focus did not like that cold start.

[Vikas]

OP:
Looks like you need a new/better battery. Also next time, take the video after having the door and hood open to capture the noise.

Subaru:
Now this is really making funny noises even after successfully catching (which should not have taken that long) If it is 2008 model, you most likely have the original battery too and could be on the last legs

 

[KrisZ]

I checked the battery over the last weekend and it was low on three cells. I topped it up just in time for another cold snap and it seems to crank a bit faster.

Had a chance to record this -24C start with some outside footage. That Zetec is pretty clunky when cold.