Is there any description of the physical characteristics of the four varnas in Scriptures?
The Yaksha asked,—"By what, 0 king, birth, behaviour, study, or learning doth a person become a Brahmana? Tell us with certitude!" Yudhishthira answered,-"Listen, 0 Yaksha! It is neither birth, nor study, nor learning, that is the cause of Brahmanahood, without doubt, it is behaviour that constitutes it. One's behaviour should always be well-guarded, especially by a Brahmana. He who maintaineth his conduct unimpaired, is never impaired himself. Professors and pupils, in fact, all who study the scriptures, if addicted to wicked habits, are to be regarded as illiterate wretches. He only is learned who performeth his religious duties. He even that hath studied the four Vedas is to be regarded as a wicked wretch scarcely distinguishable from a Sudra if his conduct be not correct. He only who performeth the Agnihotra and hath his senses under control, is called a Brahmana!"
From the above extract and the fact Yudhiṣṭhira did not tell a single full lie in his entire life, there can be no doubt that the Varṇas have no physical form whatsoever. I believe there is a slight mistranslation as it should probably read worse than a Śūdra, as the Cāturvarṇa (Cāturvarṇya?) names are all positive.
P.S. Varṇis do have a physical form, which is why Sāvarṇi is named Sāvarṇi and not Sāvarṇa. Sāvarṇa and Sāvarṇi do not come from the same source otherwise the "i" would be transformed. Being Sāvarṇa in the sense Sāvarṇi is Sāvarṇi is not possible. From subtle to gross, it goes Varṇa, then Varṇya, then Varṇi
P.P.S. The entire Yakṣa Praśna is basically showcasing the nature of a Brāhmaṇa, is short and a very good read, so you should read it yourself.
P.P.P.S. It also seems to be the only known mention of the still unnamed Yakṣopendra (I believe it is Yakṣopendra, as opposed to Yakṣopeṇdra and Indra is a Tatpuruṣa compound, but I could be wrong) (which raises a ton more questions) and is part of the engaging sub-plot of Yudhiṣṭhira secretly being a Brāhmaṇa, which makes it one of the most important stories in the entire Mahābhārata.