If you do want to overthink it, however:
He likely wouldn't have traveled through the desert regardless, but on roads. Most likely either to the coast at Jaffa and then along the coast through cities such as Caesarea and Haifa to Acre, or through Nabalus, Sebasta to Nazareth and then to Acre at the coast. It could've been done, I agree, but it'd take more than one horse, light to no equipment, no major issues along the way, they'd've had a very vaguely estimated time of arrival, because with such distances you simply cannot know if you get there a few hours earlier or later, and also, far more importantly: Isn't the city under siege and the entire country beset by huge armies?! In which case I don't entirely get how Philip could go away that easily (or why, since he'd expect their morale to falter immediately), but also, every gate would be blocked (which they would regardless at night), there'd be troops all over the place that would at the very least stop those very suspicious few riders and question them, if they're lucky, or, if they're unlucky, attack them immediately.
And crusader troops wouldn't necessarily recognise their king immediately and could expect a scheme, especially since they'd more likely assume their king to be dead, and Muslim skirmishing parties wouldn't likely be informed about the deal their sultans had made, and marauding soldiers on either side would be tempted by any riches the riders might've had on them, so riding with some crown or other would likewise have been unwise.
So traveling at night time would've possibly even been safer for them, except for the fact that it'd've had to happen at much slower pace due to the lack of light and only been possible at all with a lot of moonlight.
Which is why I say again: Don't overthink it! There's a reason why you're at chapter 38 already, and I'm only at the beginning of chapter 2 (disregarding the masterpiece of an entire book I've finished within 2 days on this forum which you haven't read, possibly because you hate comments such as this one).