It is very easy create video playlist in Youtube without logging. The trick is that, you have to create the link of your playlist manually. Here are the steps to do so.
1. The default structure of the link of a Youtube video looks like this www.youtube.com/watch?v=video1. Here, video1 is the unique ID of the video.
2. Lets assume you have to create playlist of these three video :
3. To do so, firstly, copy the unique ID part from the above 3 videos. Then create a new link in this form -
4. That's all. Now you can share this YouTube playlist link anywhere.