Is it permissible to perform tayammum for prayer after daily marital intimacy, given the cold weather and fear of illness?

Purity is a condition for the validity of prayer. Thus, whoever prays without purity, their prayer is invalid, as Allah the Almighty says: "O you who have believed, do not approach prayer while you are intoxicated until you know what you are saying or in a state of janabah, except those passing through [a prayer area], until you have washed [your whole body]. And 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 find no water, then seek clean earth and wipe over your faces and your hands [with it]. Indeed, Allah is ever Pardoning and Forgiving." And as the Prophet, peace and blessings be upon him, said: "No prayer is accepted without purification." It is not permissible for a Muslim to pray while in a state of janabah if water is available and they do not fear harm from using it. Therefore, tayammum is not permissible unless it is highly probable that harm will result from performing ghusl. In such a case, tayammum and prayer are permissible, then ghusl becomes obligatory when it is possible without harm. It is not permissible to neglect prayer due to the inability to perform ghusl.