Ski jackets, pants and shoes are different.
You can probably rent the whole clothing and shoes thng for the
skiing at the resort/ski school.
And since you probably are going for a short holiday trip.
Might be easier for you to borrow some of those puffer jackets
from friends and families.
Then you make sure your pants, tees & shoes are
suitable for layering with maybe extra 1 sizes above what you wear
in Singapore can liao.
$200/- might as well spent on longjohns, thick woolen socks and
a balaclava for sleeping.
Maybe can buy along some nice pashmina shawls to cover your neck
or just to look relatively graceful in their heated bus and
buildings. They are great as gifts too.
Go to Daiso, stock up on pairs of woolen gloves and their heated
pads that you can wear under your stocking feet in your shoes and
some in yoru pockets to keep your gloved hands warm.
If possible, opt for woolen head covers too. Heat
dissapate easily thru the head or hair. Or bring some nice
jockey caps along.