If the situation is as you mentioned, then you have done well, and may Allah reward you best and make you a good example for other mothers. (Part No. 6; Page No. 28) The people who told you that it is wrong to wake children up for prayer, are truly incorrect. We hope Allah (Exalted be He) will forgive them and guide them to encourage what is right.
It is narrated by
Abu Dawud, and
on the authority of
`Abdullah ibn `Amr (may Allah be pleased with them) that the Prophet (peace be upon him) said:
"Command your children to perform Salah (prayer) when they are seven years old, and beat them for (not offering) it when they are ten, and separate them in bed at the time of sleep.
This report is applied to all times; winter or otherwise.May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.