If you are going to use a tarp set it up on sheer poles or guy lines over the tent but not touching it. It has to be far enough away not to let any water or frost freeze to your tent.
You want to avoid the plastic bag effect where condensation just drips back onto you.
You might find banking snow around the bottom of the tarp helps insulate you, but you still need to vent the tarp enough to breath and get rid of moisture.

I don't use down bags, especially in fall or winter.
The problem is that down gets wet and then it is cold and clumpy. I recommend a decent synthetic bag instead. Even when damp the better grade synthetics are still giving some insulation value and they do dry a lot faster than down does.

One trick is to buy a small bag and then a bigger bag and use one inside the other for winter.

Put plenty of stuff under you. It does not matter what it is just as long as it is insulation. You need at least twice as much under you as you put above you.
This is after the weight of your body packs it down. (Foam pads are good here, but use plenty)

If you are allowed a fire setting your tent and tarp to take advantage of external heat can work. I usually just ended up cold with holes melted in my tarp and tent from hot sparks when I tried that and was better off with an open tarp lean-to instead of a closed tent.

About tarps:
Silnylon is pricey. I would think about getting a cheap poly tarp for winter use and keep the silnylon for summer. (Not that there is anything wrong with the nylon, just that I tend to wreck tarps when camping in winter.)

I find winter camping is about bulk more than technology, and I seem to end up packing big bags of stuff that are more air than anything. I have been toying with the idea of bubble wrap ground sheets again.