I am trying to say
Today is cold and raining, but thankfully tomorrow is sunny and a little bit cloudy.
Would this be correct?
Hoy es hace frio y llueve, pero por suerte mañana va a hace sol y un poco nublado.
Very close :)
"Correct": Hoy hace frio y está lloviendo, pero por suerte mañana estará soleado y un poco nublado (I say correct in quotes because there are many ways to say such a sentence).
You wouldn't use "es hace" because it's like "is it's", "hace frio" alone literally means "makes cold" but it is used as "it's cold".
I suppose "llueve" isn't wrong here, "Hoy llueve" is like saying "Today it rains", which is fine, but in order to match the whole "it's cold" structure I think it's a little more elegant to say "está lloviendo" which is "it's raining".
Usually if you want to say "it's sunny" you can say "está soleado" so for "it will be sunny" just change the tense "estará soleado".
Your translation has a few shortcomings:
Hoy hace frio y llueve, pero por suerte mañana va a hacer sol con alguna nube.
You cannot write va a hacer sol y un poco nublado; va a hacer nublado is not a correct construction.
At least in Spain, the construction estará soleado is unusual. We use soleado as an adjective to modify a noun (un día soleado is fine, for instance), but seldom as a predicative; we prefer the construction hacer sol, as in your own translation. So an alternative is:
Hoy hace frío y llueve, pero por suerte mañana tendremos un día soleado con alguna nube.
There is a subtle difference between algunas nubes and alguna nube; the later indicates a less cloudy day than the former. Since the original reads a little bit cloudy, I have preferred this.
The translation would be:
Hoy es un día frío y lluvioso pero por suerte mañana será (un día) soleado y un poco nublado.
Hoy hace frío y llueve. Gracias a Dios mañana va a hacer sol y algo nublado.
Creo que se puede decir de varias maneras. Aquí pongo lo que a mi me parece.