I want to hike to places like Myrdasjokull, etc. on my own without a guide in winter. Is this allowed?
I don't know when you are plannig to go to Iceland. Winter in Iceland is 6 month wide from November to May and is not the same you go in January (really cold to camp outside and almost no light) than you go in April (14 hours of light and very cold, but possible to camp with proper camp material). But these are safety reasons to do the trek or not and you ask about regulations.
A group of five people stayed last year in April in Iceland (still winter). Basically we did treks and visited public places arround the island on our own. Before to go we asked about this to the icelanic official tourism website people without response. When we were on site, we asked the same in the airport Tourist Information Center and they stated that there is no regulations about wild camping, trekking or other nature activities other than clean everything and don't enter private properties. Of course, anything you do is at your own risk and if you don't have an insurance you may end paying a lot of money for your adventure.
Anyway, if you dare to do it on your own, you will find nobody on your way except in some touristic places. We were almost alone trekking in Glymur, Krafla, Dimmuborgir, Svartifoss, Skaftafell.... The picture is when we walked on the glacier, we happen to meet the official guides and nobody of them try us to abandon our walk (sorry for the logo, I don't have the original image here).
I don't know of any rule that forbids hiking in winter. However, since Iceland is dark, cold and wet during winter months, there aren't many tourists around. You may have some difficulties getting around, not only because there are less people around but also because roads can be closed down due to heavy snow fall.
Also, finding a place to stay is harder during winter months. Again: Not too many tourists around, so some places just close down during winter and open up again in summer.
But to keep things short: Yes, it is possible to go hiking, even in winter. But it will be harder to get around.