Q: What is permissible between a husband and wife while fasting? Can we kiss? Hug?
Fasting requires abstention from food, drink, and sexual relations. The penalty for a person who breaks their fast by consciously engaging in sexual relations is very severe. However, that does not mean that all types of intimacy are prohibited between spouses while fasting. It is permissible for spouses to kiss one another while fasting and embrace one another. This is true as long as there is no fear that they will lose control of themselves and fall into that which is prohibited. However, in any case it is better that they do not do so out of desire. If they kiss or embrace out of love and care, without fear of it leading to that which is not allowed, and without any sexual desire then there is no problem with that.
It is also important to note that in such a case there should be no guilt associated with such an action. This is because it is authentically narrated that the Prophet (pbuh) used to kiss his wives while fasting.
For more info please see this article from onislam.net
And God knows best.