Hard to know exactly.
Prior to the Romans the Spanish people probably were very white looking like French people as central European people did come into Spain prior to Romans. Now the Romans themselves would have been mostly very white looking themselves. Then after Rome fell the Visigoths conquered Spain and they were white Germanic people. The Moors who were Arabs, came in when a civil war broke out among the Visigoths and conquered Spain but Berbers also came with them them who many of were white people too. Then later the Vikings began to raid Spain too and Christians who were mostly white as well. Then Arabs again.
The Spanish that went to the Americas were pretty similar genetically to the Spanish people today. But there was a constant influx of Caucasian and Arab genetics going back and forth in Spain once Rome fell. So while there's definitely an Arab influence genetically, it's relatively small compared to the total genetics. They were white genetically before Rome fell , added in some Arab genetics but also added in more white genetics along the way too. By time they went to the Americas they were pretty white looking while tending to be darker eyed and darker haired and not so pale.
I mean even today if you showed a picture of some Spanish people to a wide range of people they would probably tell you they're white people just looking at them. Sort of like not all black people have the same tone and some Arab people even look kinda white. There are variations. Heck, Native people here in the US definitely look different deepening on the tribe.