I will not guarantee it but you may have a Morton's Neuroma.
It is an inflamation of a nerve similar to carpel tunnel syndrome. Something has caused your metatarsal arch to collapse and pinch this nerve.The reason of this is usually tight shoes or tight boots. Usually the footwear is too tight in the width, but it can also happen if your foot is overly compressed top to bottom.
Make sure your shoes are nice and loose in the width of your forefoot. You shouldn't see your foot press the sides of the shoe outwards.
Make sure your boots are fitted properly. You can still have a snug fitting boot, because your foot needs to be stabilized, but be sure to have a reputable shop do a small punch that centralizes on the fifth metatarsal head of your foot. That is the knuckle where your pinky toe joins your foot. There may be a bump outsideways there. You may also need to grind or do a very very small punch for the first metatarsal head (side of big toe knuckle). You can also make sure that your foot is not being squeezed top to bottom.
I recommend these two isolated spot punches because your foot still needs support. If you buy very wide boots, or get a width expansion all the way down the length of your forefoot you will get extra motion inside your boot. This will cause your foot to slide and hit the boot, putting more pressure on the 5th metatarsal head.
The next point is very important. You NEED orthotics. Have medical grade orthotics made for your ski boots and shoes. You need two pairs, as one for shoes will not properly fit in your ski boots. The most important part of these othortics will be a small bump that goes under where that burning feeling occurs. This bump is called a Metatarsal Pad. It will lightly push upwards just behind the ball of your foot (metatarsals) and recreate the metatarsal arch. This will take the pressure off the nerve and everything will be better.
There is surgery for a Morton's Neuroma, but is has an extremely high failure rate and no one will recommend it. Wearing wide shoes, and using a metatarsal pad will allow it to be completely, or near completely, painless. Your foot will always be suceptible (sp) to a neuroma now. If you wear tight shoes, it will come back very quickly even though you hadn't felt it in months or a year.
Go ask your doctor about a Morton's Neuroma. Then go ask another doctor. SOmetimes it can be ahrd to diagnose. I know a lot of boot fitters won't get what you are talking about as it can be hard to descride.
If you have any more questions let me know.