No problem. I thought by deleting the logs, like cache, would reduce my size for loading site.
Yes, that is correct, and you should do it, But that is not doing it “at your web host end”. In many or maybe even most (I don’t know for sure) cases that is sufficient. But in some cases it will not. Only your web host can help in that case. But try it – delete all your logs and see if it results in a reduction in the size of your database.
But if you mean by “loading site” the speed at which pages load, then no, the size of the log files will not matter, except when you load the logs page.