Assuming, to judge from your English glosses, that you discard possibly non-human referents that either sentence could be applicable to, your first example does not entail that ALL the old man's hair is white, or, indeed, even that he has white hair on his head; that old man might have white hair on his chest, for example, and the sentence would still count as true. Your second sentence, on the contrary, entails that the young man's hair is blue and specifically refers to ALL the hair on his head. The difference partly hinges on the fact that the definite article "el" behaves as a sort of universal quantifier ("el pelo" = "all his hair"), but also on that, by default, if you say something about a human being's hair without further context that may instruct the hearer to interpret your statement otherwise, (s)/he will automatically assume that you mean the hair that covers the referent's head, rather than his chest, arms or whatever: after all, it is on our heads that we normally have visible hair; the hair we may have elsewhere is normally hidden, or periodically removed, and seldom referred to in our descriptions of people.
If you are also interested in the syntax of those two sentences, there is another difference, and one that corresponds with the semantics associated to each of them, but it does from a different angle from what has so far been explained.
Syntactically, "Tiene pelo blanco" is a [Tacit third person subject] + [Verb + [Direct object]] structure, and "pelo blanco" is a single syntactic constituent, as proved by the fact that it can be exhaustively replaced with "lo", as in "Lo tiene". On the contrary, "Tiene el pelo blanco" is a [Tacit 3rd. person subject] + [Verb + [[Direct Object] & [Attribute of the Direct object]]] structure, and you can choose to shorten it by replacing with "lo" either the D.O. alone or the [D.O. + At-of-D.O.] constituent. In the first case, you get "Lo tiene blanco"; in the second, you, again, get "Lo tiene".
As stated, that difference in syntax correlates with different semantic interpretations, and they differ in a respect not explained in the quick response I offered in my first paragraph. Semantically speaking, "Tiene pelo blanco" expresses a permanent property of the referent, with the peculiarities already explained above (i.e., he may have only some white hair and it need not be on his/her head, but elsewhere; again, cases in which that predicate is applicable to non-human subjects apparently do not interest you and are discarded here). As to "Tiene el pelo blanco", it expresses a property that also holds permanently, but only relative to a certain (possibly long) stage of the life of the referent, usually old age (and, again, with the peculiarities already explained: it refers, by default, to the hair on the referent's head and to all of it).
Obviously, to the extent that white, contrary to dark, blond, black, or red is not a 'normal' human hair colour (except for albino people or, for the rest of us, at a marginal stage in our life: old age), the interpretation of "Tiene el pelo blanco" also differs from that automatically triggered by "Tiene el pelo rubio/moreno/negro", etc., the 'normal' colours of human hair. [Significantly, whereas we have adjectives like "rubio", "moreno" or "pelirrojo" to describe the inherent and (relatively) permanent colour of 'normal' people's hair, as in "Es rubio/moreno/pelirrojo", we do not have a parallel adjective "blanco" that can be used in sentences like "Es blanco" to refer to an individual's having white hair throughout all/most of his life; we do have "albino" - from Latin "albus" = "white", but "Es albino" is applicable only to exceptional individuals with other unusual properties, apart from having silver-white hair, and we may ignore it here].
Hence, whereas statements like "Tiene el pelo rubio/oscuro/castaño/moreno/negro" are interpreted as expressing an inherent and permanent quality of the referent, one that holds throughout most of his life (at least until old age changes that, if it does), "Tiene el pelo blanco" MAY be interpreted as expressing a non-inherent property, one usually holding only at the later stage of the referent's life as a result of a change affecting a previous state of affairs. Of course, "tener el pelo blanco" may still be a relatively permanent property (one may have it for decades!), nothing to do with pure 'stage' properties like "Tiene el pelo verde/azul/rosa", which, if predicated of human beings, immediately suggest that they have been to the hairdresser's to get themselves a new look and may decide to dye their hair some other colour next week, but still, "Tiene el pelo blanco", if predicated of a human being, MAY express that the referent used to have dark, blond, or red hair at a previous stage and no longer does, whereas "Tiene pelo blanco" has no such implications, may apply to just some hair, and not necessarily on the referent's head, and is also more likely to be predicated of 'hairy' non-human referents.