Sounds exactly like my chanter reed when there is a sudden drop in humidity. Best not to mess with the reed. Mess with the humidity in your case and in your practice space instead.
It strikes me that if your hands are so cold that it affects your playing then perhaps your pipes are also cold… are you banished to play in the wood shed or something ?
Its always best to make the diagnosis first, before proceeding to any treatment !!
Measure humidity
Check bridle appears in right position
Assess aperture between the reed lips, are they closer than normal?
Get a feel for whether the reed is easier than usual (commonly found when notes are hard to control and things are squawking)
See if moisturiser on dry hands makes a difference.
Remember that reeds have good and bad days, good and bad weather, they are not constant as the cane is always “breathing” moisture in and out of it.
(think of how a door will in some weathers and seasons work perfectly, and at other times the same door will stick or be hard to open/close…the wood has expanded by absorbing water from the air)
It’ll help to keep a subtle amount of moisture in the pipes in general. Well enough to stop hemp in joints drying out and shrinking too much.
In extreme cases in the past I have put one into my bellows. That way the dry air going into the bellows picked up a bit of moisture from the ‘dampit’ and stopped the reeds from drying out too much.
That aside, it kind of sounds like a symptom of the binding of the reed leaking. This can be due to a sudden drop in humidity too. Re-seal it with some wax and check the sides of the reed head for leaks too.
classical double reed players have been wiring leaky reeds for hundreds of years to get more out of them,it also works on uilleann reeds as a quick fix and sometimes longer.google woodwind suppliers and order brass oboe reed wire,the finest gauge,it is cheap enough.leaks usually occur in chanter reeds at the base just below the bridle or in the mid section of the reed,if the tips are gaping,it is useless but the first 2 faults can be cured by wiring.use only one or two turns of the wire and then twist off as you would for a northumbrian bridle but be very gentle you are only seeking to close the gap, not to affect the tuning of the reed.good luck,allan.
Currently 8% humidity here in Adelaide, Australia - temperature set to get to 37°C (98°F). We have hot dry summers and cool wet winters, and so far my David Daye reed has been performing admirably in the conditions. I do find I need to mess with the bridle every now and then - I’d mark it’s current position with a pencil and try to adjust it a bit. Someone else will probably tell you my advice is terrible!