My son was 2.5 years old when he started learning how to recognize Chinese characters in books. He was too young to learn to start writing, but I slowly planted the seed of writing by showing him how to write the characters of the things around us. When we went on nature walks, I included our environment into the learning by writing in the sand, snow and with rocks.
As a little toddler, I made sure that he did lots of fine-motor skill activities, so his hands would build more dexterity to write when he is ready.
When he was around 4, he was still not interested in writing at all. He could recognize 300 Chinese characters, but still refused to write! Instead, I approached writing in a sensory way to practice learning strokes by using wool beads and hundred boards to make the characters. A popular tool in our household are sand paper character flashcards, so he can easily trace the characters with his little finger.
I often invited older children to play and learn at my house, so my son can see them write. (There’s an iPad app which can show the order of the strokes).
In my spare time, I take Chinese calligraphy and often practice at home. If you want to teach your children writing, it's best if you can write more in front of them, to show them writing is fun and enjoyable! Don't make them copy hundreds of times and make it seem like a chore!