General consensus seems to be that "school" equals school no matter what time of day you want to be there.
However, you mention a preschool, which is not covered in the school gun-free law
As for the question "Would it be OK?" - all depends on the preference of the owner/agent of the property. All I can do is point out that it's not specifically prohibited by law.§ 18.2-308.1. Possession of firearm, stun weapon, or other weapon on school property prohibited.
B. If any person possesses any firearm designed or intended to expel a projectile by action of an explosion of a combustible material while such person is upon (i) any public, private or religious elementary, middle or high school, including buildings and grounds; (ii) that portion of any property open to the public and then exclusively used for school-sponsored functions or extracurricular activities while such functions or activities are taking place; or (iii) any school bus owned or operated by any such school, he shall be guilty of a Class 6 felony; however, if the person possesses any firearm within a public, private or religious elementary, middle or high school building and intends to use, or attempts to use, such firearm, or displays such weapon in a threatening manner, such person shall be sentenced to a mandatory minimum term of imprisonment of five years to be served consecutively with any other sentence.
The exemptions set out in § 18.2-308 shall apply, mutatis mutandis, to the provisions of this section. ....