To address the questions asked, we need would to take into account the political realities of Poland at that time. One can hardly speak of 'Polish army' in mid-13th century as in theory, the existence of the country such as Poland was quite arguable after it has been partitioned by the Testimony of Bolesław III in 1138 into semi-independent provinces, in theory ruled by dukes subjected to the will of the ruler of the senioral province (Lesser Poland) but as one can imagine, it quickly devolved into the shaky alliance of provinces ruled by bickering members of the royal family. So it would be more correct to speak of 'Masovian army' or 'Silesian army' rather than Polish one, as the latter did not exist.

Now, the idea of the national army itself was different from what it is now or what has been called such since early modern times in Western Europe. In mid-13th century, Poland, as many other countries on the continent, still adhered to the chiefly feudal political organization, with the military being staffed primarily by the knights (and their retainers) bound to answer the call to arms of their seniors. Thus, the bulk of the combatants were noble landowners.

Having said this, we might now address the principal question asked. Could there be Jewish Winged Hussars among the Polish troops? This, of course, depends on how do we understand the term 'Jewish'. If we're thinking along the religious lines, this was hardly possible, as local noble status was generally granted only to Christians. In Kingdom of Poland, being a Christian was a requirement to be elevated to a noble status, but in Grand Duchy of Lithuania all converts to Christianity were granted automatic noble status since at least 1588, as the article 7 of 12th chapter of the Third Lithuanian Statute (local code of laws) issued in that year stated that 'Should any Jewish man or woman adopt the Christian faith, then from such moment onwards each such a person and all their descendats shall be treated as being noble born'. It is largely believed that such practice is much older and might reach back to second half of 15th century.

One of the first documented cases of granting nobility to Jewish converts that can be identified by name comes from the last decade of 15th century. In 1499, king Jan I granted nobility to certain Stanisław Osheyko that has been adopted to the noble family of Marcin, bishop of Miedniki, receiving the Merawa coat of arms.

On 15th April 1507, king Zygmunt I ennobled bankers from Cracow, Stefan Fiszel (also spelled Fiszl in some documents) and his two sons, Jan and Stanisław who received Korab coat of arms. Stefan also was granted the office of starosta (position more or less similar to English sheriff) of Powidz county, after which he soon adopted last name Powidzki. In the same year king also granted a noble status and the Leliwa coat of arms to Habre (Abraham) of Kiev, who has been adopted to the noble family by Jan Zabrzeszyński, Lithuanian marshall and starosta of Grodno. He subsequently adopted the last name of Józefowicz.

In 1525 an unique event took place, when the noble status has been granted to a Jew who did not convert to Christianity. It was Meir, brother of the aforementioned Abraham of Kiev, and important customs official and merchant in the Grand Duchy of Lithuania, who was granted a position of the executor general or an overseer of all the Jewish communities in the state by royal privilege of 1514, although he had to resign due to the pressure of the leaders of said communities who felt that such an office unjustly challenge their prerogatives. Meir, like his brother, assumed last name Józefowicz (changing his first name to Michał) and was adopted to the coats of arms of Leliwa, this time by Jerzy Hlebowicz, voivode of Smoleńsk. Michał Józefowicz is the only known Jewish resident of Polish-Lithuanian Commonwealth who was granted nobility without converting to Christianity.

Thus, as the Michał Józefowicz is the only known example of the Jewish noble in Polish-Lithuanian history and that he died in 1530s with his family not being famous for retaining Jewish faith (what strongly suggests that they adopted Christianity sooner or later), one can say with a good dose of certainty that there were no followers of Judaism among Polish-Lithuanian heavy cavalry, consisting of nobles and their retainers, usually also of noble birth. On the other hand, given that the Jewish converts who were ennobled usually were quite wealthy and influential, their descendants could have found their way into prestigious units, including the Armoured and Hussar regiments and thus it is almost certain that such units included some nobles whose ancestors at some point converted to Christianity in 16th or 17th century. I am not too well-versed in genealogy, but it is possible that e.g. Wincenty Józefowicz-Hlebicki using Leliwa coat of arms, a standard-bearer in Hussar unit in 1780s was a direct descendant of Abraham or Michał Józefowicz.

In addition, most Jews were subject to separate laws what somewhat is interpreted as the evidence that they formed a separate Estate, especially since mid-16th century, when they received privilege of the autonomous local administration. Urban Jews were also treated as a separate group of inhabitants, not subjected to the municipal law what was also reflected in the already mentioned Statute of Kalisz. Thus, initially they were relieved of the mandatory possession of arms and armour and participation in defence of the cities, although they often were bound to pay additional defence tax because of it. This slowly changed since late 14th century, in the wake of increasing Jewish population and level of urbanization and soon Jews were participating in the city defence as any other burgher. Jews who owned land were not expected to answer to call to arms, but Constitution of 1544 (a codification of acts, not a constitution in modern sense of this word) stipulated that Jews owning or renting the land worth between 500 and 1000 marks are bound to equip a single infantryman, and those holding land worth more had to equip one cavalryman for each 1000 marks. Less affluent Jews were usually subjected to recruitment like anyone else, and although the commoners, usually forming infantry units played secondary role in the modern Polish military (save for the aforementioned municipal defence forces) it was by all means possible to meet Jews in such units.

On the side note, one of the most famous example of the Polish-Jewish soldier, although hardly fitting in the discussed timeframe is possibly Berek (Baruch) Joselewicz, who organized and commanded light cavalry regiment composed largely of Jewish citizens of Poland and officially formed on 17th September of 1794, during the Kościuszko's Uprising. After the fall of the revolt and subsequent final partition of the Polish-Lithuanian lands, Joselewicz joined Polish Legions in Italy and took part in Napoleon's campaign in Italy, Austria and Central Europe, and was subsequently killed in the battle of Kock in 1809.

So, to sum it up, although the military presence of Jews in Poland or Grand Duchy of Lithuania was limited to the defence of the cities, since 16th century it was possible to find them also in auxiliary regular units. Jews were generally not present in the cavalry units composed of Christian nobility, although the converted Jews and their descendants who received nobility were treated like any other noble and were expected to answer to call of arms, so such people could have been found in all units, including Winged Hussar regiments.