My recommendation, and it is but a recommendation, is that you stay away from the present tense. The present tense is an extremely difficult horse to tame and if you are not feeling particularly skillful in your writing, trying to keep your head wrapped around what is not a naturally flowing literary device can get hard. Plus, many readers will move on from your story to something else when they see present tense.
If you are going for a short form, then staying with "he" and "she" as our characters' names will work. If you are going for longer forms, I advise going for names, since that tags the readers' to the characters right away.
This is what it would look like with just a minimal change:
A cool summer breeze drifted across the moonlit courtyard, as a man crossed the wide space heading for the darkened porch, pebbles crunching under foot. He paused before the aging door. This place was eerie, not known to him before then, yet it felt oddly familiar and somewhat comforting. This was not the reason he paused, as he was used to oddly familiar. It was because he knew somehow in his heart that she would be waiting for him. He did not pause out of fear, but because he knew that he would leave the moment his eyes met hers, whether that was his intention or not. Glancing at the reflection in the darkened glass that was not his own, he brushed off an almost imperceptible speck of dust from his shirt and turned the cold iron handle.
Stepping into the large open entrance hall was like plunging himself into the frozen waters of the arctic, the warm fragrant summer air replaced with a frigid and almost chemical atmosphere. His breath would be clouds of mist, but he does not breathe.
The sound of glass clinking together falls on his ears, but he has little time to wonder what it may be, for now the echoes of bare footsteps hold his attention. He follows them with his eyes through the walls above.
She stepped out onto the landing above the entrance hall, her long dress stirring in the breeze caused by her motion. Her unblemished skin was a pallid moonlight white; it shone against the black silk of her attire. She was slender, tall and other-worldly beautiful, he tore his eyes away from her body and with trepidation moved his gaze towards her face. Long shimmering black hair fell over her shoulders and down the sensual curves of her clavicle, in contrast her high thin eyebrows were so fair they were almost non existent, long black lashes framed her vivid silver eyes. Her eyes which are so loving, so familiar locked onto his own, he tried to speak.
His own helpless cry awakened him...
In trying to keep that "otherworldy" feel of the present tense, I left one segment in the present just as the character made a transition from one dream stage to another. See what you think...
The premise sounds interesting, a man who dreams of a hard to reach lover, maybe... A man who seeks a lost one through "borrowing" dreams... Lots of great concepts to play with. Keep writing. It gets harder as you go, but it feels good to do it.