Opinions please..

Getting ready to spend on the anvil for the tire hammer.  Since hot rolled 1018 is cheaper than cold, my question is whether the increased tensile strength, brinell hardness, etc. of cold-rolled is worth the extra cost for the role of this part.  Does it matter?  It's a spendy chunk of steel and don't want to throw $ away on specs I don't need.

It makes no difference, assuming of course that the anvil mass is caped with appropriately hardened alloy dies.  So save your money, hot rolled 1018/A36 is fine.  Do try and get above the 10:1 tup/anvil ratio though!