DD, who will be four next month, was dry during the day for a couple of months when we decided to start at night. Waiting it out while she wore a diaper at night didn't work for us--she would not even be asleep yet and the diaper would already be wet. Maybe it was a novelty after spending all day focusing on being dry, to be back in a diaper at night. But fifteen minutes or so after her night diaper went on, she needed to be changed. So we just went cold turkey.
Around mid-April we put a plastic sheet on DD's toddler bed, and started using just a simple blanket to sleep on top of (no sheets), with another blanket on top of her to keep her warm. We have stacks of blankets that can be used for this purpose, so it's easy to throw one set off the bed and put another on.
For a month DD was wet every single morning. We took off the bedding, rinsed DD and said that she was great at staying dry during the day, and it was harder to learn to listen to her body at night, but it would happen. Sporadically she began to go through the night dry.
Now, about two months later, DD is dry six nights out of seven. We don't wake her at all, even though I'm up past midnight every night. We used to wake her sometimes but she would occasionally get really irritated and have a hard time going back to sleep, and washing bedding was preferable to dealing with a middle-of-the-night tantrum. Plus, we didn't want her dependent on us, rather than her own body, to wake her to pee.
It's a long process; unpack your patience and dust it off--if you do go with our method you are going to need it!