Whether or not it’s wrong to become sexually and emotionally involved with another person, while married, is ultimately up to you, your husband and your value systems. While there are people who certainly have strong opinions on this matter, what is right/wrong impacts you and what’s best for you and your spouse. Some couples, separated or not, are able to successfully navigate being involved with other people thanks to open communication, rules of engagement, and both having a firm handle on jealousy tendencies. Depending on the reason for separation, e.g., infidelity, some couples agree that this test period is one where seeing others is allowed, and that any extramarital relationships will not be revealed or will need to be part of the process of figuring out if they truly are "'til death do you part."
In figuring out next steps, do some soul-searching, reflecting on why you got married, and what it means to have made vows that are typically considered “null and void” only once divorce papers have been signed. Talk to your husband about expectations during this separation, including seeing other people. His reaction and thoughts could be all the answer you need to get involved with this other man or not. If your husband is dead set against both of you being sexually and/or emotionally involved with others, and to the point that this would determine your chances of reconciliation, then you need to decide what you want now – versus in the future – and what’s best for you given everything that has led up to this difficult time in your marriage.
Thank you for your question and good luck!