All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad, sallallaahu 'alayhi wa sallam, is His slave and Messenger.
The scholars held different opinions regarding the ruling on the discharges released by women as to whether they are ritually pure in general or the ruling varies based on different criteria. The preponderant opinion adopted at Islamweb is that discharges coming out from the childbirth canal are ritually pure, while discharges coming out from the urinary tract are ritually impure. These discharges invalidate ablution according to the opinion of most scholars, and this is the preponderant opinion and the one adopted at Islamweb.
If the water is cold, you should heat it. If you are unable to heat the water, and you fear that using cold water would harm you, then wash as many of the body parts that should be washed in ablution as you can and perform Tayammum (dry ablution) for the rest by striking the soil with your both hands and then wiping your face and hands up to the wrist.
Ibn Qudaamah said in Al-Mughni: “If one fears extreme cold and he can heat the water or use it in a manner that protects him from harm – like washing the body parts (that should be washed in ablution) one after the other and once he washes an organ, he covers it – then he is obliged to do so. If he is unable to do so, then, according to the view of most scholars, he may perform Tayammum and pray.” [End of Quote]
Allah Knows best.