Is ablution considered valid despite being unable to wipe the entire head, wiping the ears consecutively with the left hand, washing the face and pouring water on the feet with the left hand, and wiping over only one sock, and what is the correct way to perform ablution in this health condition, especially on cold days?

The religion of Allah is ease and is built upon alleviation and removing hardship. So, whoever is unable to perform an obligation, it is either waived for them or they move to its substitute.

Ablution (Wudu') is valid if its pillars are fulfilled: intention, order, washing the face, washing the hands up to the elbows, wiping the head, and washing the feet up to the ankles.

Wiping part of the head is sufficient due to your inability, and this is the view of Ash-Shafi'i and Abu Hanifa.

Wiping the ears with one hand is permissible.

Washing the face with one hand is permissible, provided the washing is comprehensive.

Washing the feet is obligatory if possible, and wiping over socks is not permissible if one is unable to wipe them.

If it is possible to wipe one sock and part of the other, that is permissible.

If you are unable to wash some limbs, wash what you can and perform tayammum (definition) (dry ablution) for the rest, or wash what is possible and nothing is required of you for the rest, according to a differing opinion.

If an ailment prevents the use of water for some limbs, one washes what is possible and performs tayammum for the rest.