Allah says in (5:6):
... And if you are in a state of janabah, then purify yourselves. But if you are ill or on a journey or one of you comes from the place of relieving himself or you have contacted women and do not find water, then seek clean earth and wipe over your faces and hands with it. Allah does not intend to make difficulty for you, but He intends to purify you and complete His favor upon you that you may be grateful.
So the verse clearly say that a major condition for the permission of tayammum is the need or the absence of water.
On the other Allah also says that we should neither harm nor kill ourselves:
And spend in the way of Allah and do not throw [yourselves] with your [own] hands into destruction [by refraining]. And do good; indeed, Allah loves the doers of good. (2:195)
... And do not kill yourselves [or one another]. Indeed, Allah is to you ever Merciful. (4:29)
And HE says that we are allowed to do something prohibited in case of necessity (under some conditions which explain the necessity):
And why should you not eat of that upon which the name of Allah has been mentioned while He has explained in detail to you what He has forbidden you, excepting that to which you are compelled. ... (6:119)
This means if you have water you should use it unless using it would make you sick or may harm you. But you must be aware that you'll have the option to use warm or hot water for wudu' and ghusl! If you reject it for no good reason at least you would commit a sin.
So far the legal basis for you to make your decision!
Here's a fatwa on the topic islamqa #70507.