Both white tea and green teas that are called Silver Needles are not quite suitable for people with cold TCM body type, the green tea more so. If you do not want to waste the tea you already bought, drink it in the early afternoon, say around 3 when the bodily heat is higher after lunch is pretty much digested.
White tea White Peony (again there are green tea varieties of White Peony) is a better choice as a white tea for health benefits for people with cold TCM body type. Matured ones are the safest, so are those from Zhenghe, which are more oxidized than those from elsewhere. White Peony is cheaper than Silver Needles too.
