(NOTE: I have edited this to reflect additional information about Philmont requirements, as described in a post further below this one.)

If we're starting entirely from scratch, here's a stab at a list of NECESSARY items:

a pack (and a way to keep its contents dry in the rain)
a tent (as per Philmont rule)
tarp to cover pack at night (as per Philmont rule)
a sleeping bag (or quilt or blankets) warm down to 20F
insulation underneath while sleeping (sleeping pad, clothing piled up)

cooking pot
stove and fuel (Philmont rule: cannot be alcohol-based)
eating utensil
water container
optional: a water purification method

toothbrush
light source (flashlight, LED pinchlight, LED headlamp, etc)
whistle (best way to be found when lost)
optional: pocket knife (usu. part of Ten Essentials)

personal rain protection (poncho, rain suit, etc)
warm hat (fleece, wool, etc)
torso warmth layer (fleece, wool, etc)
wind-blocking layer (rain suit, nylon wind breaker, etc)
gloves (too cold to go without these)

footwear (boots, shoes)
sox (probably wool)
pants (not denim, please)
shirt (polyester, please)
underwear

Note: the clothing system needs to be 100% adequate to prevent hypothermia in cold weather with some rain. That probably means something more than just one of every clothing item listed above.