Welcome, Sohail Si. The Wittgenstein Palace was certainly a domain of culture but I can find no evidence of a philosophical presence among the familiy's friends and visitors. Others may be better informed but I have checked Ray Monk's biography and Edward Kanterian's Wittgenstein (2007).
We do know, however, that the young Wittgenstein read Schopenhauer and Nietzsche.
'Professor Anscombe says that when Wittgenstein was sixteen he had read Schopenhauer "and had been
greatly impressed by Schopenhauer's theory of the 'world as
idea' (though not by the 'world as will')"' - A. Phillips Griffiths, 'Wittgenstein and the Four-Fold Root of the Principle of
Sufficient Reason', Proceedings of the Aristotelian Society, Supplementary Volumes , 1976, Vol. 50
(1976), pp. 1-20: 3; E. Anscombe, An Introduction to Wittgenstein's Tractatus: 11.
Kanterian ascribes to the yong Witttgenstein an admiration for Nietzsche (Kanterian: 25). Wittgenstein quoted from Thus Spake Zarathustra in his conversations with Rush Rhees: : Ludwig Wittgenstein, Rush Rhees and Gabriel Citron, 'Wittgenstein's Philosophical Conversations with Rush Rhees (1939–50): From the Notes of
Rush Rhees', Mind, Vol. 124, No. 493 (January 2015), pp. 1-71: 52).
Wittgenstein read Weininger's Sex and Character (1903). The book is marred by anti-semitism and certain views about women. According to Kanterian, it was not not these views that interested Wittgenstein:
'It was rather Weininger's views on men and modernity, and the more general ethical questions Weininger raised that (as Wittgenstein tried to explain later to his puzzled Cambridge friends) - Kanterian: 26-7.
Boltzmann & Hertz
'... towards the end of his school days Wittgnstein considered studying with Ludwig Boltlzmann in Vienna. Boltzmann was a prominent physicist who had invented statistical mechanics, but who was also known for his lectures on the philosophy of physics, some of which were published in his Popular Writings in 1905 and which Wittgenstein read. He also read the introduction to Heinrich Hertz's famous Principles of Mechanics (1894). Both Boltzmann and Hertz operated within a broady Kantian framework, according to which science is a model constructed by the human mind that does not refer to or describe reality, but rather is used to organize empirical data in one among several possible ways' - Kanterian: 30.
Kanterian misleads us here. Boltzmann stressed the hypothetical nature of knowledge and was not aligned to Kant in the way he suggests. Paul Feyerabend sets the record a little straighter:
'The reasons Boltzmann gave for his dissatisfaction with dogmatic systems of thought were partly biological, partly logical. Boltzmann's biological argument took the followong lines. Our ideas are the result of a process of adaptation by trial and error (Boltzmann was an enthusiastic follower of Darwin ...). Some of these ideas, such as the Euclidean character of space, may be "inborn" in the sense that the individual is endowed with them through the development of the speces. Such an origin explains their force, the impression of incorrigibility, but "it would be a fallacy to assume, as Kant did, that they are therefore absolutely correct'. The future development of the species, aided by scientific research, may lead to further modifications and to further improvement.' (P. Feyerabend, 'Boltzmann, Ludwig (1844-1906)', The Encyclopedia of Philosophy, vols 1 & 2, ed. Paul Edwards, NY: Macmillan, 1972: 334.)
The logical argument concluded that 'the edifice of our theories does not consist of ... irrefutable truths ... It consists of largely arbitary elements ... so-called hypotheses' (Feyerabend: 335.) Hypnosifl (comment below) is correct to sugguest that in some respects Botlzmann anticipates what became in later in the 2oth century the hypothetical-deductive method.
So although Wittgenstein does not appear to have become personally acquainted with philosophers in the cultural life of the family home, he did make acquaintance with philosophy.