Here is a quote from another forum: http://bushcraftusa.com/forum/showthread.php/83737-Floating-your-fire-in-deeeeep-snow
"Let's say the snow is way too deep to dig out.
How do you float your fire?
Especially when its a warming fire that you will need all night?
Personally, I stamp down the area, then do 3 layers of alternating pine boughs and snow, much larger than the actual fire area, then a pedestal of at least 2 layers of whole green logs, also larger than the expected fire size."
If you want to not leave a trace, you can often find fallen over trees from winter storms and cut the green branches off them.
I think that a folding saw and a hatchet is excessive. The whole point of a hatchet or axe is that you can crosscut and split with it. If you are already carrying a saw for crosscutting, a sturdy knife is going to be great for splitting.
The utility of a fire is very underestimated on this forum. I almost always cook over a fire so I don't carry any weight in fuel or a stove. I can cook things that take longer to cook and would waste a ton of fuel, things like baking or raw pasta. With a nice fire, you don't need to carry a bunch of warm camp clothing. Just a light mid layer is good, you don't need a huge puffy. With those two things considered, the weight of a folding saw and fixed blade is justified.
Also, I have spent more nights that I want to admit curled up next to a fire. I spent an entire week doing that every night because my sleep system ended up not being warm enough. I have seen so many trip reports where people shivered all night or bailed because they were too cold. Stoking a fire is a bit tedious, but it feels so nice to be warmed by something other than your own body heat. It's VERY effective. Throw some big logs on the fire and you should get a few hours before having to throw on more. I'm not saying you should do this intentionally, but having the ability to do it could save you from some unexpectedly cold nights.