Can you explain the rattle a little ?
the location you think the rattle is coming from
and the "type" of rattle would be helpful.
(does it sound metallic, like a tin can) or maybe like a piece of plastic rattling in a cup or what?
let me know and I will give you a good possibility of what is likely causing it.
I think its from the engine, its a metallic rattle (A bit like a tappet). If you drive the car, stop and turn engine off while (like go into the shops) come back, start engine it runs fine, its just on initial COLD start
In very COLD temps it's not uncommon engines to be louder in general. If the noise is not just a more audible version of regular engine noise then you could in fact be hearing a rattle coming from a heat shield or a timing chain tensioner.
The easiest thing to do would be to have someoneone help you pinpoint the exact location by lightly reving the engine in neutral on a cold morning. If the noise is immediate before driving anywhere and remedies itself then it could be tensioner related.
Now if the noise is more like you say where it comes on during light acceleration, then it's much more likely to be something like a heat shield which is much more susceptible to vibrations at lower loads.
Let me know how else i can help please.