I think there's a difference between 'to go out to play' and 'to go out and play'. If you say they go out TO play, you say that they went outside just to play, and that their plan was to play all along. On the other hand, if you say they go out AND play you say they go out, and then they decide to play now that they're outside already. In the first sentence, them going out is dependant on their plan to play, while in the second sentence these two actions are independent from eachother.
Thanks for your comment. It sounds possible, but very theoretical. It's just that I have never noticed this in English, to combine two verbs with 'and', in the way that we do in Swedish ALL THE TIME, without ever thinking that there are any difference in meaning, and we don't use the infintivie, while in English it is an 'infinitive' either way (no visible conjugation). -- Is there any native English speakers who can comment?
I think it is less common in english to do so, and more common to combine them with 'to' instead, however, there still is a difference. It's not much of a difference since the actions still are the same, but the difference does exist and if you decided to be very critical then you would make a difference between those two. Or maybe I'm just prejudiced because we make quite of a difference there in german.
It sounds very natural to me as a native English speaker (Irish/Scottish). As sumuenkeli said, there is a subtle difference between 'go out to play' and 'go out and play', but both could be used in the same context and mean basically the same thing. Using 'to' implies a logical connection between the activities, with one leading to the other, while 'and' implies you're doing both at the same time. You would 'go out to eat and drink' for example, 'he can read and write', but 'she learns to read', and 'I drink to forget'. I could drink 'and' forget too I suppose, but that slightly implies that the forgetting is independent of the drinking and not a result of it.