'Frightening' and 'frightful' are both adjectives based on the same root, but they have different meanings. 'Frightening' means 'scary'. A horror movie is frightening. A fast drive down an icy mountain road is frightening. 'Frightful' just means very bad. It's a rather outdated word which can be applied anything which the speaker finds particularly unpleasant. The nearest synonym is 'horrible'. The dictionary says that this is mainly British and also quite old-fashioned, which maybe explains why some of the other members couldn't answer your question. There is also an American song from the 1940s called 'Let it Snow!' which begins with the words 'The weather outside is frightful'. It's still popular today, especially around Christmas time: https://www.youtube.com/watch?v=mN7LW0Y00kE

We would say the cold was frightful to mean it was very unpleasant - we really didn’t feel good about the cold. And we would say the cold was frightening to mean that we were scared of what the cold could do to us.

Let’s put the two adjectives into context to better understand them. I hiked up a mountain this weekend, lost my balance and almost fell down the mountain. It was a very frightening experience. In this context ‘frightening’ means that the idea of almost falling down the mountain made the person feel very afraid or scared - so we use this word when something makes us feel scared. I had dinner with my friend’s family and they were all shouting at each other in a very frightful manner the whole time. I felt uncomfortable and just wanted to leave. In this context ‘frightful’ means that experiencing people shouting at each other is an extremely unpleasant or uncomfortable feeling. You don’t get scared but you really don’t feel good about it and really want it to stop.

[frightful = unpleasant] [frightening = terrifying] New Oxford American Dictionary frightful | ˈfraɪtfəl | adjective chiefly British very unpleasant, serious, or shocking: there's been a frightful accident. • informal used for emphasis, especially of something bad: her hair was a frightful mess. frightening | ˈfraɪt(ə)nɪŋ | adjective making someone afraid or anxious; terrifying: a frightening experience.

A dictionary search where they give example sentences is a valuable resource and option to explore first. Frightful is a bit outdated = very bad. "The poor dear girl she is in a frightful mess, since the death of her father" = a somewhat outdated sentences you may hear on old films etc.