I plan on exercising by running barefoot. Is this safe?

Is it safe to walk across a motorway with 4 lanes either side?

With most things concerning personal safety if you have to ask then it's probably not safe for you.

I never asked about such things even as a child, I could pretty much judge the situation on the fly.  People that can't usually end up dead or injured while blaming someone else for their ineptitude.

thats not very smart

Some people do all their running barefoot (or a good portion of it). Do some research on barefoot running so you can be aware of possible issues. Of course you need to be careful of the running surface and ensure you don't step on anything that could cause injury. If you are new to barefoot running, ease into it. 

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I did a quick search on 'barefoot running 101' and found the below article. There were others as well, that you may find helpful so be sure and do a search and read all you can - the pros and cons of it. 

Not on the roads, but on grass or sand is fine

In general, yes, if you take precautions.

You would have to watch out for hazards, such as broken glass or sharp metal.

You also have to train gradually. Start by walking on asphalt. Do a little at first, and gradually increase the amount. This is to toughen up the skin on your feet.

You also need to gradually train your bones, muscles, tendons, and ligaments. You can start with some running on grass. (But, grass can conceal sharp objects.)  

When your feet are toughened up, start training on your regular surfaces. Again,  start with a little and gradually increase the distance.

If you are currently a runner, do your regular workouts in shoes. When making the transition, take off your shoes near the end of a workout and finish barefoot. Gradually lengthen the barefoot distance and shorten the shoe-wearing distance.

I'm assuming you have no biomechanical or other issues that will increase risk of barefoot running.  If, for example, you should run with an orthosis (orthotic), running barefoot might not be safe, since shoes are needed to hold the orthosis in place. 

An alternative is minimalist shoe running. Minimalist shoes are very light weight. Running in them is close to barefoot running, but they offer a little more protection. And, they might be able to hold orthoses. If you do use an orthosis, you might need a different one when using minimalist shoes.

Comment: Abebe Bikila won the 1960 Olympic Marathon running barefoot.

Comment: I tried making the transition from running in shoes to barefoot a few years ago. But, there was some sort of weakness and I was unable to train my left foot to not crash the heel onto the running surface.

Comment: There was a surge in barefoot running popularity about 15 years ago. Barefoot runners do run on the street. I talked to a barefoot runner when we were near mile 20 in a marathon. The course was mostly asphalt. 

Parkour practitioners think bare feet are the best shoes. 

If it’s on the street, I wouldn’t. There could be broken glasses and other sharp objects on the ground. If you developed enough callus you might be fine. Animals don’t wear shoes but they have thick pads that gives them protection. 

Maybe you can ask Cody from Dual Survival. The guy is a survivalist expert and he doesn’t wear shoes unless there’s snow. I think he might have worn shoes when he was stranded in the desert.