Stop!!! Do not play your wood piccolo in its current condition.
In the extremes of very cold, very dry weather, wood instruments dry out and the wood shrinks. In these circumstances, playing it introduces warm, moist air into the bore.
This sets up the perfect conditions to crack your piccolo. The warm air and moisture from your breath cause the interior bore to expand faster than the exterior. When the inside expands faster than the exterior, something has give and a crack can form to release the stress.
Your piccolo is in drastic need of an intervention and needs to be hydrated. Here is an easy way to do it. You need the following items:
A plastic container with a lid - you just need one larger than the piccolo

- Plastic Bin.jpg (9.58 KiB) Viewed 7005 times
and a cake cooling rack to fit inside the bin.

- Cooling rack.jpg (95.12 KiB) Viewed 7005 times
Place a little water in the bottom of the plastic bin. Place the cooling rack inside, feet down, to create a platform inside the plastic bin. Be sure that the water level is lower the the rack. If need be, place a couple of blocks (wood, styrofoam, etc.) under the rack to elevate it a bit higher. Place your unassembled piccolo on the rack. Place the lid on the plastic bin to keep the moisture inside. Leave the piccolo in the bin for several days. Check it every two days or so to see if the metal end ring has tightened and the water has not all evaporated. When the ring is tight again, leave the piccolo in the bin for two more days. After that, it should be safe to play it again, but take it slow to give the piccolo a chance to go through a break-in period and acclimate to being played again.
In your climate, you may need to repeat this several times each year.