Most photographers prefer to do it in the morning (I was told 8:30 am by several photographers too when I was checking around) for two reasons - 1) the light is better than during mid-day and 2) it doesn't interfere with any wedding ceremonies/receptions that normally take place in the afternoon and evening.
However, you don't have to do it the morning after the wedding and in hearing from many brides on here, most choose to do it a few days later and all photographers are generally accommodating of this...if yours is not, honestly, you may wanna consider someone else who is! Our photographer is doing ours almost 6 days later (we're staying 2 weeks) on the morning of our choice because he takes you to a private beach for the whole morning and we didn't want to be away from our friends and family that long. You should have the choice of morning...ya wanna be able to celebrate the night of the night of the wedding and not worry about getting up early and/or being a little hungover
And I doubt the water will be cold...I've yet to be down South any experience anything close to cold water, regardless of time of day