Get your scarves, mittens and socks & pullover woolen hats
from Daiso. They have a small wall selling winter stuff.
Get at least two sets of thermal wear with socks, at least for
wearing to sleep, or when you are outdoors often.
Make sure your shoes, pants are bigger size then what you
normally wear in Singapore.
Jacket wise, as what FireIce typed. Dont buy it too tight
across the body, cos you might want to layer it some more,
depending on how you feel about the weather there.
Lastly, bring lots of thin cotton long sleeve tees that absorbs
sweat and can dry quickly. I have 1/2 dozen with me for
travelling always.
And because my body temp is higher, I only needed to wear a
padded vest for messing around with snow in a Canandian ski
resort. The arms arent restricted by the padded sleeves.
And make sure your jacket comes with a waterproof hood.
Helps to ward off rain and snow from melting into your hair.